Statistics Questions

Age of Westminster investor in years Part 2 Under 35 35 49 50 7 102 Total Risky 15 11 90 0 808 18 20 40 0 282 18 18 70 0 026 51 Moderate mixed 13 a Determine the type of test statistic to use Type of test statistic Chi square 15 63 0 443 24 26 80 0 293 30 24 57 1 200 67 Conservative 7 7 47 0 030 18 12 80 2 113 7 11 73 1 907 32 Degrees of freedom 4 c Find the p value Round to three or more decimal places 0 130 Total 35 Answer the following to summarize the test of the hypothesis that there is no relationship between t variables age of Westminster investor and riskiness of investment choice for this past year For your the 0 05 level of significance 60 55 150 b Find the value of the test statistic Round to two or more decimal places d Can we reject the hypothesis that there is no relationship between the variables age of Westminster investor and riskiness of investment choice for this past year Use the 0 05 level of significance X

Much is still to be learned about the relationship between sound frequency and loudness One way to study the relationship between sound frequency and loudness is to have listeners perform loudness judgments for tones of different frequencies For each listener the output of these judgments is a number measured in sones that gives the loudness of the tone relative to the loudness of a reference tone Suppose that you have in front of you data from an experimental study in which listeners were asked to perform such loudness judgments for tones of various intensities and frequencies The listeners were divided into non overlapping groups according to their hearing ability normal unaided hearing some hearing loss at certain 0 frequencies normal aided hearing etc The data give the sone measurements for each listener You perform a one way independent samples ANOVA test of the hypothesis that the mean sone measurement are equal for the different populations of listeners represented in the study a This ANOVA test is summarized in the ANOVA table below Fill in the missing value of this ANOVA table Round your answer to at least two decimal places Source of Degrees of Sum of variation freedom squares Between groups Error within groups Total 4 60 64 2 61 15 48 18 09 Mean square X 0 65 b How many listeners total were tested in the experiment 10 X 0 26 X F statistic c For the ANOVA test it is assumed that the population variances of sone values for this tone are equal for each population of listeners represented What is an unbiased estimate of this common population variance based on the sample variances 0 X S d What is the p value corresponding to the F statistic for the ANOVA test Round your answer to at least three decimal places e Using the 0 01 level of significance do you conclude that there are differences in the mean sone values for this tone for the three populations of listeners

scientist has read that the mean birth weight of babies born at full term is 7 3 pounds The scientist has good eason to believe that the mean birth weight of babies born at full term is different from this value and plans to erform a statistical test She selects a random sample of birth weights of babies born at full term and finds the mean of the sample to be 7 5 pounds and the standard deviation to be 1 8 pounds Based on this information complete the parts below a What are the null hypothesis Ho and the alternative hypothesis H that should be used for the test Ho HO b Suppose that the scientist decides not to reject the null hypothesis What sort of error might she be making Choose one c Suppose the true mean birth weight of babies born at full term is 7 3 pounds Fill in the blanks to describe a Type I error A Type I error would be Choose one Choose one Choose one Choose one the hypothesis that when in fact u is 0 0 020 X X OSO 0 0 O

A consumer products testing group is evaluating two competing brands of tires Brand 1 and Brand 2 Though the two brands have been comparable in the past some technological advances were recently made in the Brand 2 manufacturing process and the consumer group is testing to see if Brand 2 will outperform Brand 1 Tread wear can vary considerably depending on the type of car and the group is trying to eliminate this effect by installing the two brands on the same 12 cars chosen at random In particular each car has one tire of each brand on its front wheels with half of the cars chosen at random to have Brand 1 on the left front wheel and the rest to have Brand there After all of the cars are driven over the standard test course for 20 000 miles the amount of tread wear in inches is recorded as shown in the table below Car Brand 1 Brand 2 1 2 4 Difference Brand 1 Brand 2 Send data to calculator 5 0 46 0 35 0 46 0 37 0 34 0 53 0 33 0 49 0 25 0 27 6 7 0 33 8 0 46 0 54 0 43 0 61 0 41 0 48 9 a State the null hypothesis Ho and the alternative hypothesis H HO H 0 b Determine the type of test statistic to use Type of test statistic Choose one c Find the value of the test statistic Round to three or more decimal places 0 10 d Find the critical value at the 0 10 level of significance Round to three or more decimal places 0 07 0 02 0 03 0 12 0 07 0 13 0 13 0 05 0 30 0 19 0 01 e At the 0 10 level can the consumer group conclude that the mean tread wear of Brand 1 exceeds that of Brand 2 Yes No 0 48 0 35 0 31 0 29 0 34 11 Based on these data can the consumer group conclude at the 0 10 level of significance that the mean tread wear of Brand 1 exceeds that of Brand 2 Answer this question by performing a hypothesis test regarding which is u with a letter d subscript the population mean difference in tread wear for the two brands of tires Assume that this population of differences Brand 1 minus Brand 2 is normally distributed Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified If necessary consult a list of formulas x X 0 0 Ox a S 12 OSO 0 62 0 33 0 29 P Olo NO O

A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs model A and model B Independent random samples of the two models were taken Analysis of 9 bulbs of model A showed a mean lifetime of 1358 hours and a standard deviation of 107 hours Analysis of 15 bulbs of model B showed a mean lifetime of 1369 hours and a standard deviation of 114 hours Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal Construct a 95 confidence interval for the difference between the mean lifetime of model A bulbs and the mean lifetime of model B bulbs Then find the lower limit and upper limit of the 95 confidence interval Carry your intermediate computations to at least three decimal places Round your responses to at least two decimal places If necessary consult a list of formulas Lower limit Upper limit X S EEN

Find both the x intercept and the y intercept of the line given by this equation 6 7x 8 8y 5 6 0 Round your answers to two decimal places a x intercept b y intercept X 5

Find the median of the following sample 7 2 5 3 6 8 mean and varianci

3 For what value of C is for C 4 x probability density function on 2 27

A continuous random variable X has probability density function given by I 3 x fox Find E X X 0 x 0

4 Let X be density functions 1 24x 2 4 fwr O Find variance V x of X a random variable having otherwise

A data set includes 106 body temperatures of healthy adult humans having a mean of 98 9 F and a standard deviation of 0 63 F Construct a 99 confidence interval estimate of the mean body temperature of all healthy humans What does the sample suggest about the use of 98 6 F as the mean body temperature Click here to view a t distribution table Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table What is the confidence interval estimate of the population mean F H F Round to three decimal places as needed

A researcher believes that about 71 of the seeds planted with the aid of a new chemical fertilizer will germinate He chooses a random sample of 135 seeds and plants them with the aid of the fertilizer Assuming his belief to be true approximate the probability that more than 95 of the 135 seeds will germinate Use the normal approximation to the binomial with a correction for continuity Round your answer to at least three decimal places Do not round any intermediate steps If necessary consult a list of formulas

Use the accompanying radiation levels W for 50 different cell phones Find the percentile P25 kg W P25 Type an integer or a decimal Do not round kg 0 24 0 88 1 07 1 22 1 37 0 24 0 89 1 11 1 23 1 39 0 28 0 90 1 12 1 23 1 39 0 45 0 90 1 13 1 29 1 40 0 61 0 95 1 14 1 32 1 46 0 61 0 97 1 16 1 32 1 48 0 61 1 02 1 18 1 33 1 48 0 63 1 03 1 19 1 34 1 53 0 72 1 04 1 20 1 36 1 53 Save 0 81 1 05 1 21 1 37 1 54 0

K Households are randomly selected and partitioned into groups of four For those groups the random variable x is the number of households with a printer Determine whether a probability distribution is given If a probability distribution is given find its mean and standard deviation If a probability distribution is not given identify the requirements that are not satisfied Does the table show a probability distribution Select all that apply A Yes the table shows a probability distribution B No the random variable x is categorical instead of numerical C No the numerical values of the random variable x are not associated with probabilities D No not every probability is between 0 and 1 inclusive E No the sum of all the probabilities is not equal to 1 Find the mean of the random variable x Select the correct choice below and if necessary fill in the answer box to complete your choice CA 24 household s BOOS Round to one decimal place as needed OB The table does not show a probability distribution Find the standard deviation of the random variable x Select the correct choice below and if necessary fill in the answer box to complete your choice OA o household s Round to one decimal place as needed OB The table does not show a probability distribution X 0 Save P x C 0 022 1 0 148 2 0 343 3 0 354 4 0 133 e

Consider the following data set awesomeness rating ID 1 2 3 4 LO 5 6 7 2 38 4 14 1 2 2 1 7 62 7 78 3 09 The sample mean of awesomeness is closest to 04 187371 03 472171 02 518571 01 564971 02 995371 02 041771 The sample range of awesomeness is closest to 13 3504 16 9264 8 344 10 132 11 92 09 0592 The sample median value of awesomeness is closest to 00 7112 03 0952 01 9032 02 38

A cognitive scientist wants to test whether there is any difference in puzzle solving abilities between crows and sparrows Independent samples of ten crows and seven sparrows were chosen at random The crows took a mean of 35 minutes to solve a certain puzzle with a standard deviation of 4 1 minutes The sparrows took a mean of 36 minutes to solve the same puzzle with a standard deviation of 4 3 minutes Assume that the two populations of completion times are normally distributed and that the population variances ar equal Can we conclude at the 0 01 level of significance that u the mean puzzle solving times for crows is less than the mean puzzle solving times for sparrows Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the table If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 d Find the critical value at the 0 01 level of significance Round to three or more decimal places e Can we conclude that the mean puzzle solving times for crows is less than the mean puzzle solving times for sparrows H x X O S X 00 P p 010 0 0 030 020 8 0 0 0 0 0 0

Suppose you are the president of the student government You wish to conduct a survey to determine the student body s opinion regarding student services The administration provides you with a list of the names and phone numbers of the 414 registered students a Discuss a procedure you could follow to obtain a simple random sample of 5 students b Obtain this sample Click the icon to view the portion of the random number table CITTLE a Which of the following procedures could you follow to obtain a simple random sample of 5 students Select all that apply A List the names in alphabetical order and take the first five names on the list B List each name on a separate piece of paper place them all in a hat and pick five C Number the names from 1 to 414 and use a random number table to produce 5 different three digit numbers corresponding to the names selected D Ask the students to come to a meeting and pick five from those who come to the meeting

A club wants to sponsor a panel discussion on the upcoming national election The club wants four of its members to lead the panel discussion Write a short description of the processes that can be used to generate your sample Obtain a simple random sample of size 4 from the table Click the icon to view the club membership list Which of the following would produce a simple random sample Select all that apply A Vote on which four members should lead the panel discussion and select those four B List each name on a separate piece of paper place them all in a hat and pick four C Number the names from 1 to 25 and use a random number table to produce 4 different two digit numbers corresponding to the names selected D List the members in alphabetical order and take the first four names on the list

As part of a college literature course students must select three classic works of literature from the provided list and complete critical book reviews for each selected work Write a short description of the processes that can be used to generate a simple random sample of three books Obtain a simple random sample of size 3 from this list Click the icon to view the classic works list Which of the following would produce a simple random sample Select all that apply A List each book on a separate piece of paper place them all in a hat and pick three B Number the books from 1 to 9 and use a random number table to produce 3 different one digit numbers corresponding to the books selected C List the names in alphabetical order and take the first three on the list D Ask someone their opinion on which three books are best and select those three

Choose the correct answer below OA Once an individual is selected the individual can be selected again OB Once an individual is selected the individual cannot be selected again Once a sample is taken those individuals are no longer considered part of the population Once a sample is taken those individuals cannot be selected for any other samples O C D

What is a frame Choose the correct answer below OA A frame is the population being studied OB A frame is a list of the individuals in the sample being studied OC A frame is a list of the individuals in the population being studied D A frame is the sample taken from the population being studied

In a particular survey of internet users 3745 respondents say that they use social networking sites and 1434 respondents say that they do not use social networking sites What is the probability that a randomly selected person uses a social networking site Does that result suggest that it is likely with a probability of 0 5 or greater for someone to use social networking sites The probability that a randomly selected person uses a social networking site is Round to three decimal places as needed G

Choose the correct answer below OA A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring The sample is then called a simple random sample O B Simple random sampling is the process of selecting individuals from a population using a convenient sample The sample is then called a simple random sample OC Simple random sampling is the process of obtaining a sample of size n from a population of the same size n The sample is then called a simple random sample O D Simple random sampling is the process of using chance to select individuals from a population to be included in the sample The sample is then called a simple random sample

The uni sity data uters computer I and computer 2 A new routine has recently been written for computer 1 to handle its tasks while computer 2 is still using the preexisting routine The center wants to determine if the processing time for computer 1 s tasks is now less than that of computer 2 A random sample of 11 processing times from computer 1 showed a mean of 37 seconds with a standard deviation of 17 seconds while a random sample of 9 processing times from computer 2 chosen independently of those for computer 1 showed a mean of 56 seconds with a standard deviation of 20 seconds Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal A Can we conclude at the 0 05 level of significance that the mean processing time of computer 1 is less than the mean processing time of computer 2 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the table If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H H 0 H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places e Can we conclude that the mean processing time of computer 1 is less than the mean processing time of computer 2 E pl x X 5 0 0 O X S 2 P 0 0 OSO 20 O O Q 00 O O Aa V

Duseholds are randomly selected and partitioned into groups of four For those groups the random variable x is the number of households with a printer Determine whether a probability distribution is given If a probability distribution is given find s mean and standard deviation If a probability distribution is not given identify the requirements that are not satisfied Does the table show a probability distribution Select all that apply A Yes the table shows a probability distribution B No the random variable x is categorical instead of numerical C No the numerical values of the random variable x are not associated with probabilities D No not every probability is between 0 and 1 inclusive CILS X P x D 0 0 022 1 0 148 2 0 343 3 0 354 4 0 133 xat

the given values The tallest living man at one time had a height of 241 cm The shortest living man at that time had a height of 59 1 cm Heights of men at that time had a mean of 172 93 cm and a standard deviation of 6 59 cm Which of these two men had the height th more extreme Since the z score for the tallest man is z Round to two decimal places and the z score for the shortest man is z the RECCER man had the height that was more extreme shortest

Here are 6 celebrities with some of the highest net worths in millions of dollars in a recent year George Lucas 5500 Oprah Winfrey 3200 Michael Jordan 1700 J K Rowling 1000 David Copperfield 1000 and Jerry Seinfeld 950 Find the range variance and standard deviation for the sample data What do the results tell us about the population of all celebrities Based on the nature of the amounts what can be inferred about their precision The range is 4550 million Round to the nearest integer as needed The variance is 3315750 million dollars squared Round to the nearest integer as needed The standard deviation is 1821 million Round to the nearest integer as needed What do the results tell us about the population of all celebrities A Because the data are from celebrities with the highest net worths the measures of variation are not at all typical for all celebrities OB Because the statistics are calculated from the data the measures of variation cannot tell us about other celebrities OC Because the statistics are calculated from the data the measures of variation are typical for all celebrities D Because the data are from celebrities with the highest net worths the measures of variation are typical for all celebrities Based on the nature of the amounts what can be inferred about their precision Because all of the amounts end with 0 it appears that they are rounded to the nearest hundred thousand dollars GEEEE so it would make sense to round the results to the nearest hundred million dollars million dollars 4 e

The lengths of your statistics class has a continuous uniform distribution between 46 minutes and 58 minutes Let X be the length of a class in minutes If one section is randomly selected answer the following questions a What is the distribution of X X Please show the following answers to 4 decimal places b What is the probability that the class is exactly 52 minutes long c What is the probability that the class is more than 52 minutes long d What is the probability that the class is between 49 minutes and 53 minutes long e What is the probability that the class is less than 49 minutes or more than 53 minutes long

14 18 Listed below are the numbers of hurricanes that occurred in each year in a certain region The data are listed in order by year Find the range variance and standard deviation for the given sample data Include appropriate units in the results What important feature of the data is not revealed by any of the measures of variation The range of the sample data is 16 hurricanes Round to one decimal place as needed 9 11 The standard deviation of the sample data is 5 0 hurricanes Round to one decimal place as needed The variance of the sample data is Round to one decimal 13 14 13 5 BREED Points 0 57 of 2 4 12 10 2 Save 3

effectiveness of two drug treatments on patients with a chronic mental illness Treatment 1 has been around for many years while treatment 2 has recently been developed based on the latest research The researchers chose two independent test groups The first group had 13 patients all of whom received treatment 1 and had a mean time until remission of 181 days with a standard deviation of 6 days The second group had 11 patients all of whom received treatment 2 and had a mean time until remission of 180 days with a standard deviation of 7 days Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance Can we conclude at the 0 01 level of significance that the mean M27 number of days until remission after treatment 1 is greater than the mean number of days until remission after treatment 2 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the table If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 d Find the critical value at the 0 01 level of significance Round to three or more decimal places 0 e Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2 OYes No H x 5 X a S 2 OSO 0 0 P G Q olo 030 0

What is an observational study What is a designed experiment Which allows the researcher to claim causation between an explanatory variable and a response variable What is an observational study OA An observational study is when a researcher assigns individuals to a certain group intentionally changing the value of an explanatory variable and then recording the value of the response variable for each group B An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables OC An observational study is a list of all individuals in a population along with certain characteristics of each individual What is a designed experiment OA A designed experiment is when a researcher assigns individuals to a certain group intentionally changing the value of an explanatory variable and then recording the value of the response variable for each group OB A designed experiment measures the value of the response variable without attempting to influence the value of either the response or explanatory variables OC A designed experiment is a list of all individuals in a population along with certain characteristics of each individual

4 3 Find the a mean b median c mode and d midrange for the given sample data An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas Listed below are the phenotype codes where 1 smooth yellow 2 smooth green 3 wrinkled yellow and 4 wrinkled green Do the results make sense 2 a The mean phenotype code is 2 9 Round to the nearest tenth as needed b The median phenotype code is Type an integer or a decimal 3 3 4 2 3 EXCE 1 3 0 4 01 2 4 4 3 2 5 C Save

a Find the mean The mean is 156 million Type an integer or a decimal rounded to one decimal place as needed b Find the median Find the a mean b median c mode and d midrange for the data and then e answer the given questions Listed below are the highest amounts of net worth in millions of dollars of all celebrities What do the results tell us about the population of all celebrities Based on the nature of the amounts what can be inferred about their precision 230 190 175 155 145 145 130 130 130 130 130 The median is 145 million Type an integer or a decimal rounded to one decimal place as needed c Find the mode Select the correct choice below and if necessary fill in the answer box to complete your choice Part 3 of 6 A The mode s is are million Type an integer or a decimal Do not round Use a comma to separate answers as needed OB There is no mode Points 0 33 of 2 C 2 53 67 30 points

A web page design firm has two designs for an online hardware store To determine which is the more effective design the firm uses one page with only teenage visitors and a second page with only adult visitors For each visit the firm records the visitor s rating on the layout and the number of items viewed Complete parts a through c below b What are the two response variables For each response variable state whether it is qualitative or quantitative Select all that apply A One response variable is the number of items viewed This response variable is quantitative B One response variable is the web page design This response variable is qualitative C One response variable is the visitor s rating on the layout This response variable is qualitative D One response variable is the age group This response variable is qualitative c Explain how confounding might be an issue with this study Choose the correct answer below OA Since the variables are not all quantitative or all qualitative they may interact causing the results to be misleading or incorrect OB Since there is only one explanatory variable and two response variables the explanatory variable will not affect both response variables equally resulting in misleading results OC Since there are two response variables in this study they may interact causing the results to be misleading or incorrect O D Since the designs are being tested with two different age groups preferences depending on the age group may groups

OA A lurking variable is a quantitative variable that has an infinite number of possible values that are not countable In addition lurking variables are typically very large numbers that make them difficult if not impossible to include in a study OB A lurking variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values In addition lurking variables are typically equal to zero or almost equal to zero C A lurking variable is an explanatory variable that was not considered in a study but that affects the value of the response variable in the study In addition lurking variables are typically related to explanatory variables in the study OD A lurking variable is a response variable that was not considered in a study but is also affected by the casual relationship of the explanatory variables in the study In addition lurking variables are typically related to response variables in the study What is a confounding variable OA A confounding variable is a response variable that was not considered in a study whose effect cannot be distinguished from a second explanatory variable in the study OB A confounding variable is the explanatory variable on which a study has been focused OC A confounding variable is an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study OD A confounding variable is a response variable that has an effect on the explanatory variable but it cannot be accurately measured in the study

Explain what is meant by confounding What is a lurking variable What is a confounding variable effects of the response variable When there is zero confounding in a study the effects of the response variable are entirely caused by the effects of the explanatory variable Oc Confounding in a study occurs when there is little or no actual relationship between the explanatory and response variable other than random chance This sometimes causes completely unrelated variables to appear to have a causal relationship and can cause variables that have almost no relationship to have a very strong relationship D Confounding in a study occurs when the effects of two or more explanatory variables are not separated Therefore any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study What is a lurking variable OA A lurking variable is a quantitative variable that has an infinite number of possible values that are not countable In addition lurking variables are typically very large numbers that make them difficult if not impossible to include in a study OB A lurking variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values In addition lurking variables are typically equal to zero or almost equal to zero OC A lurking variable is an explanatory variable that was not considered in a study but that affects the value of the response variable in the study In addition lurking variables are typically related to explanatory variables in the study OD A lurking variable is a response variable that was not considered in a study but is also affected by the casual relationship of the explanatory variables in the study In addition lurking variables are typically related to response variables in the study

Researchers wanted to know if there is a link between proximity to high tension wires and the rate of leukemia in children To conduct the study researchers compared the rate of leukemia for children who lived within 1 2 mile of high tension wires to the rate of leukemia for children who did not live within 1 2 mile of high tension wires The researchers found that the rate of leukemia for children near high tension wires was higher than the rate for those not near high tension wires Can the researchers conclude that proximity with high tension wires causes leukemia in children This is a reading assessment question Be certain of your answer because you only get one attempt on this question SEX O A No because this is an observational study OB No because this is a designed experiment OC Yes because this is a designed experiment which allow for statements of causality OD Yes because this is an observational studies which allow for statements of causality

64 of all violent felons in the prison system are repeat offenders If 42 violent felons are randomly selected find the probability that a Exactly 27 of them are repeat offenders b At most 29 of them are repeat offenders c At least 28 of them are repeat offenders d Between 22 and 29 including 22 and 29 of them are repeat offenders Round all answers to 4 decimal places

Suppose that you randomly selected 26 adults Assume 19 of the population smoke Use exact values for the mean and the standard deviation Round all answers to 2 decimal places a Using the Range Rule of Thumb what is the minimum number of usual smokers we can expect to get out of 26 adults b Using the Range Rule of Thumb what is the maximum number of usual smokers we can expect to get out of 26 adults

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender Complete parts a to c below Number of Number of Male Fatal Licensed Age Drivers 000s 16 12 16 20 21 24 25 34 6 424 6 930 18 068 35 44 20 406 45 54 19 898 55 64 14 311 65 74 8 194 74 4 803 Crashes Males 227 5 180 5 016 8 596 7 990 7 139 4 527 2 274 2 022 Number of Female Fatal Licensed Drivers 000s 12 6 139 6 816 Number of 17 664 20 070 19 984 14 441 8 371 5 375 Crashes Females 77 2 113 1 520 2 780 2 742 2 285 1 514 938 955 b Interpret the slope of the least squares regression line for each gender if appropriate How might an insurance company use this information What is the correct interpretation of the slope of the least squares regression line for males Select the correct choice below and if necessary fill in the answer box to complete your choice Y OA If the number of fatal crashes increases by 1 then the number of female licensed drivers increases by thousand on average Round to three decimal places as needed OB If the average age of all female licensed drivers increases by 1 then the number of fatal crashes increases by on average Round to three decimal places as needed OC If the number of female licensed drivers increases by 1 thousand then the number of fatal crashes increases by on average Round to three decimal places as needed OD It does not make sense to interpret the slope

For the accompanying data set a draw a scatter diagram of the data b by hand compute the correlation coefficient and c determine whether there is a linear relation between x and y X y 2 4 n 3 0 997 4 0 950 5 0 878 Critical Values for Correlation Coefficient 6 7 0 811 0 754 8 0 707 9 0 666 10 0 632 11 0 602 12 0 576 4 8 13 0 553 14 0 532 15 0 514 6 12 6 12 7 20 16 0 497 17 0 482 18 0 468 19 0 456 20 0 444 21 0 433 22 0 423 23 0 413 24 0 404 25 0 396 26 0 388 27 0 381 28 0 374 29 0 367 30 0 361 n b By hand compute the correlation coefficient The correlation coefficient is r Round to three decimal places as needed c Determine whether there is a linear relation between x and y Because the correlation coefficient is correlation coefficient is and the absolute value of the than the critical value for this data set linear relation exists between x and y

hoose the correct answer below when a residual is positive OA A residual is the difference between an observed value of the response variable y anc the average value of the response variable If it is positive then the response variable greater than the mean OB A residual is the difference between an observed value of the response variable y anc the predicted value of y If it is positive then the observed value is greater than the predicted value C A residual is the difference between an observed value of the response variable y and the value of the corresponding explanatory variable x If it is positive then the respons variable is greater than the explanatory variable D A residual is a data point that does not fit the pattern of the rest of the data If it is positive then the data point should still be included in the data set

tch the coefficient of determination to the tter diagram The scales on the x axis y axis are the same for each scatter gram R2 0 27 b R2 0 94 c R 1 Scatter diagram Scatter diagram Scatter diagram III CIE E Response Response Response Explam Explan Explan

Researchers initiated a long term study of the population of American black bears One aspect of the study was to develop a model that could be used to predict a bear s weight since it is not practical to weigh bears in the field One variable thought to be related to weight is the length of the bear The accompanying data represent the lengths and weights of 12 American black bears Complete parts a through d below b Draw a scatter diagram of the data Choose the correct graph below Total Length cm 139 0 135 0 139 0 120 5 149 0 141 0 141 0 150 0 166 0 151 5 129 5 150 0 Weight kg 110 60 90 60 85 100 110 85 155 140 105 110 Critical Values for Correlation Coefficient n 3 0 997 4 0 950 5 0 878 6 0 811 7 0 754 8 0 707 9 0 666 10 0 632 11 0 602 12 0 576 13 0 553 14 0 532 15 0514 16 0 497 17 0 482 18 0 468 19 0 456 20 0 444 21 0 433 22 0 423 23 0 413 24 0 404 25 0 396 26 0 388 27 0381 28 0 374 29 0 367 OA A Weight kg 180 40 100 AM ES 200 Length cm OB Q Q AWeight kg 180 40 100 OTO 200 Length cm Q Q 2 O C AWeight kg 180 40 100 33 200 Length cm Q Q O D ALength cm 180 40 100 200 Weight kg

ermine whether the scatter diagram indicates a linear relation may exist between the two ables If the relation is linear determine ther it indicates a positive or negative ociation between the variables this information to answer the following BI Response 30 20 10 04 ine aata points do not nave a linear relationship because they do not lie mainly in a straight line e two variables have a positive or a negative association UU The two variables have a negative association The two variables have a positive association None of the above 20 Explanatory 40 ine data points nave a linea relationship because they de mainly in a straight line

etermine whether the scatter diagram indicates mat a linear relation may exist between the two ariables If the relation is linear determine hether it indicates a positive or negative ssociation between the variables Ise this information to answer the following o the two variables have a linear relationship OA The data points have a linear relationship because they lie mainly in a straight line OC The data points do not have a linear relationship because they do not lie mainly in a straight line Response 30 20 10 OB 0 8 20 Explanatory the two variables have a positive or a negative association 8 40 The data points do not have a linear relationship because they lie mainly straight line OD The data points have a linear relationship because they do not lie mainly in a straight line

Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness Treatment 1 has been around for many years while treatment 2 has recently been developed based on the latest research The researchers chose two independent test groups The first group had 14 patients all of whom received treatment 1 and had a mean time until remission of 169 days with a standard deviation of 7 days The second group had 11 patients all of whom received treatment 2 and had a mean time until remission of 161 days with a standard deviation of 5 days Assume that the populations of times until remission for each of the two treatments are normally distributed with equal var ance F Can we conclude at the 0 01 level of significance that the mean number of days until remission after treatment 1 is greater than the mean number of days until remission after treatment 2 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the table If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 d Find the p value Round to three or more decimal places 0 e Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2 P xl O S X 0 0 0 0 P p 0 0 OSO 020 ola 0

In a cohort study of 300 members of the Leisurely Loafers Club who took a vacation to the Bahamas 170 became infected with giardiasis One hundred twenty nine 129 who swam in a resort pool became ill and 94 who did not swim did not become ill Set up the 2x2 table and calculate the appropriate rate of risk

An industrial plant wants to determine which of two types of fuel electric or gas is more cost efficient measured in cost per unit of energy Independent random samples were taken of plants using electricity and plants using gas These samples consisted of 12 plants using electricity which had a mean cost per unit of 36 40 and standard deviation of 8 50 and 15 plants using gas which had a mean of 45 20 and standard deviation of 7 88 Assume that the populations of costs per unit are normally distributed for each type of fuel and assume that the variances of these populations are equal Can we conclude at the 0 05 level of significance that the mean cost per unit for plants using electricity differs from 2 the mean cost per unit for plants using gas Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the table If necessary consult a list of formulas a State the null hypothesis H and the alternative hypothesis H Ho H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the two critical values at the 0 05 level of significance Round to three or more decimal places and e Can we conclude that the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas ON ON X 0 0 O X S P 0 0 o 0 0 OSO 020 nin 0 0

The accompanying data set lists diastolic blood pressure measurements mm Hg of females All of the values are even numbers Construct a stemplot Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest These values are often used to find the median 66 80 62 88 88 66 72 60 80 74 90 66 78 94 68 64 70 64 74 90 68 60 74 72 Construct the stemplot 6 0024466688 70224448 80088 9 004 Sav The two values that are closest to the middle when the data are sorted in order from lowest to highest are and Type integers or decimals Do not round Use ascending order