Statistics Questions and Answers

2 Party Republican Democrat Female Male 115 103 179 105 150 150 Independent Is there an association between party affiliation and gender a Construct a frequency marginal distribution b Construct a relative frequency marginal distribution c What proportion of registered voters considers themselves to be Independent d Construct a conditional distribution of party affiliation by gender e Draw a bar graph of the conditional distribution found in part d f Is gender associated with party affiliation If so how

Complete parts a through h for the data below 40 70 80 D 63 46 33 X y 30 30 y 50 60 58 53 X 90 b Find the equation of the line containing the points 50 58 and 80 33 0 30 299 3 or simplified fractions 90 304 0 100

A survey asks questions about one s happiness and health One would think that health plays a role in one s happiness Use the data in the accompanying table to determine whether healthier people tend to also be happier Treat level of health as the explanatory variable Click the icon to view the data table Create a conditional distribution for the data Level of Happiness Not too happy Pretty happy Very happy Total M Data table Poor Not too happy happy Poor 694 950 Level of Health Fair Fair 1 366 3 817 1002 Good Good 1 629 9 642 4 520 Excellent Excellent 742 5 185 5 095 C X Clear all

One of the biggest factors in determining the value of a home is the square footage The accompanying data represent the square footage and selling price in thousands of dollars for a random sample of homes for sale in a certain region Complete parts a through h below Click the icon to view the housing data FEED c Determine the linear correlation coefficient between square footage and asking price r 0 913 Round to three decimal places as needed d Is there a linear relation between square footage and asking price Yes No e Find the least squares regression line treating square footage as the explanatory varia y x Round the slope to three decimal places as needed Round the intercept to one decimal Data Table Square Footage x 2189 3223 1155 2064 3237 2654 4270 2235 2550 1744 1844 3986 Selling Price 5000s 377 4 380 7 194 1 1 352 640 1 351 6 652 4 380 9 415 8 303 9 279 9 717 7

23 What is the score at the 40th percentile point

A survey of 1030 randomly selected registered United States voters was conducted in which survey participants were asked What is your political affiliation Results of the survey by gender are shown below Complete parts a and b below Political Affiliation Gender Female Male Democrat 270 146 Independent 182 109 a Complete the following statement In the contingency table shown the Republican 151 172 This is a reading assessment question Be certain of your answer because you only get one attempt on this question variable is gender and the variable is political affiliation

What is the coefficient of determination for Data Set B X 3 6 8 3 0 5 1 4 8 2 Data Set A y 5 9 4 3 8 3 0 3 6 8 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 Data Set B X 3 1 W765911 14 9 4 1 2 2000N 1 0 9 0 5 0 3 4 7 4 0 1 7 5 y 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 X 2 8 IN o 3 o 8 1 Full Data Set Data Set C 03 3 0 8 3 8 2 755 1 4 1 0 7 9 066 5 9 5 0 y 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 This is a reading assessment question Be certain of your answer because you only get one attempt on this question The coefficient of determination for Data Set B is Type an integer or decimal rounded to the nearest tenth as needed

e data set given in the accompanying table Complete parts a through d Click the icon to view the data table a Construct a frequency marginal distribution Y Y Marginal distribution X 20 30 X2 25 25 X3 30 50 Marginal distribution Data table Y Y2 4 X 20 30 X2 25 25 X3 30 50 C

Complete parts a through h for the data below X 40 70 80 O y 63 46 33 UA Ay 90 30 30 50 58 x 60 53 90 oo 5 B y Type integers or simplified fractions Ay 100 04 b Find the equation of the line containing the points 50 58 and 80 33 30 90 O G L OC 90 304 4 100 3 O G

set is given below a Draw a scatter diagram Comment on the type of relation that appears to exist between x and y b Given that x 3 6667 sx 2 5820 y 3 8167 sy 1 8236 and r 0 9543 determine the least squares regression line c Graph the least squares regression line on the scatter diagram drawn in part a 0 X y 0 1 4 5 6 5 6 6 2 4 3 2 7 1 9 6 2 2 0 C There appears to be a linear negative relationship b x Round to three decimal places as needed 0 Q 0 0 Q

Complete parts a through h for the data below 60 70 X 40 63 80 D 33 46 53 y UA 90 30 50 58 0 100 NUEZ 90 B 100 100 30 BETER d By hand determine the least squares regression line y x D Round to three decimal places as needed 30 3 90 90 30 30 90 Q Q

Complete parts a through h for the data below 3 4 7 8 7 10 19 22 X y OA Ay 10 0 0 5 12 X 10 OU C B AY 30 0 0 10 b Find the equation of the line containing the points 3 7 and 8 22 y x Tyne integers or simplified fractions CH Ay 30 04 0 10 O o Q OD 10 0 0 Ax Y 30 Q O 17

Recently a random sample of 13 18 year olds was asked How much do you currently have in savings The data in the table represent the responses to the survey Approximate the mean and standard deviation amount of savings Click the icon to view the frequency distribution for the amount of savings The sample mean amount of savings is 229 Round to the nearest dollar as needed The sample standard deviation is S Round to the nearest dollar as needed Frequency distribution of amount of savings Savings 0 199 200 399 400 599 600 799 800 999 1000 1199 1200 1399 Frequency 333 94 50 19 9 8 1 F X

Nature of Science 3 Interpreting Data Univariate Statistics Question 6 Which data set is represented by the box plot Select one 50 51 54 55 55 58 60 68 75 75 76 87 87 89 99 57 58 67 70 74 82 84 85 86 88 91 93 95 100 100 57 63 65 65 66 70 76 78 84 88 92 93 94 100 100 56 58 68 69 70 80 83 84 85 86 86 91 91 98 98 57 65 78 93 100

The list below shows the average monthly temperatures in degrees Fahrenheit in Ahmed s city for the past year 01 74 86 90 68 76 64 68 84 90 94 82 92 Which box and whisker plot correctly represents the data in the list Select one Average Monthly Temperatures 64 64 74 Average Monthly Temperatures 64 74 HHH 64 84 74 84 Average Monthly Temperatures 74 84 94 84 94 Average Monthly Temperatures 94 94

In a Leichtman Research Group survey of 1150 TV households 75 1 of them had at least one Internet connected TV device for example Smart TV standalone streaming device connected video game console A marketing executive wants to convey high penetration of Internet connected TV devices so he makes the claim tha percentage of all homes with at least one Internet connected TV device is equal to 82 Test that claim using a 0 05 significance level Use the P value method Use the normal distribution as an approximation to the binomial distribution Let p denote the population proportion of all homes with at least one Internet connected TV device Identify the null and alternative hypotheses Ho P 0 82 H P 0 82 Type integers or decimals Do not round Identify the test statistic 2 0 Round to two decimal places as needed

cher studying public opinion of proposed Social Security changes obtains a si ample of 50 adult Americans and asks them whether or not they support the To say that the distribution of the sample proportion of adults who respond y ately normal how many more adult Americans does the researcher need to s ing cases of all adult Americans support the changes of all adult Americans support the changes esearcher must ask esearcher must ask more American adults Round up to the nearest integ more American adults Round up to the nearest integ

When she was 9 years of age a girl did a science fair experiment in which she tested professional touch therapists to see if they could sense coin to select either her right hand or her left hand and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it Among 280 trials the touch therapists were correct 123 times Use a 0 10 significance level to test the claim that touch therapists use a method equivalent to random guesses Do the results suggest that touch therapists are effective wyprawy wy Identify the test statistic 2 2 03 Round to two decimal places as needed Identify the P value P value 0 042 Round to three decimal places as needed State the conclusion about the null hypothesis as well as the final conclusion that addresses the original claim Address whether the results suggest that touch therapists are effective The results sufficient evidence to the null hypotheses There that touch therapists are effective the claim that touch therapists use a method equivalent to random guesses

A certain drug is used to treat asthma In a clinical trial of the drug 20 of 292 treated subjects experienced headaches based on data from the manufacturer The accompanying calculator display shows results from a test of the claim that less than 10 of treated subjects experienced headaches Use the normal distribution as an approximation to the binomial distribution and assume a 0 01 significance level to complete parts a through e below Ho p 01 H p 0 1 Decide whether to reject the null hypothesis Choose the correct answer below A Fail to reject the null hypothesis because the P value is greater than the significance level a B Reject the null hypothesis because the P value is less than or equal to the significance level a OC Fail to reject the null hypotheses because the P value is less than or equal to the significance level a ber ne the P value is greater than the significance level ir 1 PropzTest prop 0 1 2 1 794530924 p 0 0363562614 p 0 0684931507 n 292

mpped a When she was 9 years of age a girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy coin to select either her right hand or her left hand and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it Among 280 trials the touch therapists were correct 123 times Use a 0 10 significance level to test the claim that touch therapists use a method equivalent to random guesses Do the results suggest that touch therapists are effective Let p denote the population proportion of correct hand selections by touch therapists Identify the null and alternative hypotheses to test the claim that touch therapists use a method equivalent to random guesses Ho P 0 50 H P 0 50 Type integers or decimals Do not round Identify the test statistic z 2 03 Round to two decimal places as needed Identify the P value P value Round to three decimal places as needed

Trials in an experiment with a polygraph include 97 results that include 24 cases of wrong results and 73 cases of correct results Use a 0 01 significance level to test the claim that such polygraph results are correct less than 80 of the time Identify the null hypothesis alternative hypothesis test statistic P value conclusion about the null hypothesis and final conclusion that addresses the original claim Use the P value method Use the normal distribution as an approximation of the binomial distribution OA Ho p 0 20 H p 0 20 OC Ho p 0 20 H p 0 20 OE H P 0 80 H p 0 80 B Ho p 0 80 H p 0 80 OD Ho p 0 20 H p 0 20 OF H p 0 80 H p 0 80 The test statistic is z 1 17 Round to two decimal places as needed The P value is 0 1210 Round to four decimal places as needed Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim Ho There sufficient evidence to support the claim that the polygraph results are correct less than 80 of the time

men she was 9 years of age a girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field She flipped a min to select either her right hand or her left hand and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it Among 280 trials the touch therapists were correct 123 times Use a 0 10 significance level to test the claim that touch therapists use a method quivalent to random guesses Do the results suggest that touch therapists are effective Let p denote the population proportion of correct hand selections by touch therapists Identify the null and alternative hypotheses to test the claim that touch therapists use a method equivalent to random guesses Ho P H P nals Do not round

s used to treat asthma In a clinical trial of the drug 21 of 258 treated subjects experienced headaches based on data from er The accompanying calculator display shows results from a test of the claim that less than 12 of treated subjects experienced se the normal distribution as an approximation to the binomial distribution and assume a 0 01 significance level to complete gh e below p 0 12 0 P 0 12 whether to reject the null hypothesis Choose the correct answer below Fail to reject the null hypothesis because the P value is less than or equal to the significance level c Fail to reject the null hypothesis because the P value is greater than the significance level a Reject the null hypothesis because the P value is greater than the significance level a al to the significance level a 1 PropZTest prop 0 12 Z 1 908172033 p 0 0281844925 p 0 0813953488 n 258

Listed below are altitudes thousands of feet and outside air temperatures F recorded during a flight Find the a explained variation b unexplained variation and c indicated prediction interval There is sufficient evidence to support a claim of a linear correlation so it is reasonable to use the regression equation when making predictions For the prediction interval use a 95 confidence level with the altitude of 6327 ft or 6 327 thousand feet Altitude Temperature a Find the explained variation 3 60 Round to two decimal places as needed 7 34 16 24 19 9 27 28 31 41 32 59

Q Q x G E No because the graph has multiple peaks F No because the graph is always greater than or equal to zero G Yes because the graph satisfies all of the criteria for a normal curve H No because the highest point of the graph occurs at the mean

e amount of time adults spend watching television is closely monitored by firms because ps to determine advertising pricing for commercials Complete parts a through d Do you think the variable weekly time spent watching television would be mally distributed If not what shape would you expect the variable to have A The variable weekly time spent watching television is likely skewed right not norma distributed B The variable weekly time spent watching television is likely normally distributed C The variable weekly time spent watching television is likely skewed left not normally distributed D The variable weekly time spent watching television is likely uniform not normally distributed E The variable weekly time spent watching television is likely symmetric but not norma distributed

2 A Yes because the graph may not satisfy all of the criteria for a normal curve be satisfies at least one of the criteria B No because the graph is not always greater than or equal to zero C No because the highest point of the graph does not occur at the median n

se the results from a survey of a simple random sample of 1073 adults Among the 1073 respondents 68 rated themselves as above average drivers We want to test 13 20 Claim that of adults rate themselves as above average drivers Complete parts a through c a Identify the actual number of respondents who rated themselves as above average drivers Round to the nearest whole number as needed

Dose the lengths of human pregnancies are normally distributed with 266 days and a Complete parts a and b below The figure to the right represents the normal curve with 266 days and a 16 days The area to the right of X 285 is 75 Provide two interpretations of this area wide one interpretation of the area using the given values act the correct choice below and fill in the answer boxes to plete your choice e integers or decimals A The proportion of human pregnancies that last less than days is 3 The proportion of human pregnancies that last more than days is s 266 285 O O B

b According to a certain survey adults spend 2 25 hours per day watching television on weekday Assume that the standard deviation for time spent watching television on a wee 1 93 hours If a random sample of 40 adults is obtained describe the sampling distribution the mean amount of time spent watching television on a weekday and o R c te TH with is approximately normal mplete parts a through d d dom sample of 40 adults results in a mean time wat nd 3 hours cimal places as needed of the Internet is that it is thought to reduce televisio has a uniform distribution d watching Suppose that a random sample of 35 individuals who

e the correct answer below false rue

Listed below are foot lengths mm and heights mm of males Find the regression equation letting foot length be the predictor x variable Fin the best predicted height of a male with a foot length of 273 1 mm How does the result compare to the actual height of 1776 mm Foot Length 282 0 277 7 252 8 259 2 279 4 257 8 274 2 261 8 G Height 1785 1 1770 9 1676 1 1645 9 1858 7 1710 4 1788 7 1737 0 The regression equation is y x Round the y intercept to the nearest integer as needed Round the slope to two decimal places as needed

Listed below are the numbers of cricket chirps in 1 minute and the corresponding temperatures in F Find the regression equation letting chirps 1 minute be the independent x variable Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute using the regression equation What is wrong with this predicted temperature Chirps in 1 min Temperature F 982 80 1177 980 1127 774 1210 885 753 74 8 64 4 85 2 82 7 89 8 64 6 86 3 The regression equation is y 27 4 0 0518 x Round the y intercept to one decimal place as needed Round the slope to four decimal places as needed The best predicted temperature at a time when a cricket chirps 3000 times in 1 minute based on the regression equation is 74 8 F Round to the nearest integer as needed

a Let g x 6 a f t dt where fis the function whose graph is shown f LA Evaluate g 4 Show work t

35 lb The water taxi has a stated capacity of 25 passengers and the water taxi was rated for a load limit of 3750 lb Complete parts a through d below engers from harbor to another Assume that weights of passengers are normally distributed with a mean of 194 lb and a standard deviation The maximum mean weight is lb Type an integer or a decimal Do not round 0 of 1 a Given that the water taxi was rated for a load limit of 3750 lb what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity 25 passengers CELLE Save

12 Suppose a simple random sample of size 36 is selected from a population of size 1 044 with mean 8 and standard deviation 1 If the sampling distribution of x is constructed what is the expected value of x In other words what is the value of Answer Continue Deget answer

op 0 11 The sampling distribution of p is given below Find p 0 P P 0 2 Answer 1 3 0 6 2 3 0 2 Round your answer to the nearest thousandths

Question 8 of 17 8 Find the variance of the small population data set 0 1 0 1 0 1 0 0 1 0 Answer

1 Use graphing technology where applicable to answer the following questions A neurologist wishes to determine if age affects how quickly a person reacts in a stressful situation such as being asked on the spot to talk about themselves for a minute Data on the ages and reaction times of a group of randomly chosen people are collected and shown below Age years 10 12 12 15 19 22 25 26 29 32 32 35 38 Reaction Time seconds 8 7 5 8 7 6 5 6 5 4 4 5 3 5 3 3 2 8 a Create a scatter plot and determine the line of best fit c Pr d Predic Comm may in

y page of your document For each of the following questions identify whether it involves one variable analysis or two variable analys whether the variable s are discrete or continuous What are the 4 most popular songs played on the radio last week b How does the amount of fertilizer affect plant growth c How did the students in Mr Datahead s class perform in the recent Data Management test

Let the predictor variable x represent heights of males and let response variable y represent weights of males A sample of 143 heights and weights results in se 16 28265 cm In your own words describe what that value of se represents Choose the correct answer below OA The value of s is the standard deviation of e which is a measure of the differences between the observed weights and the weights predicted from the regression equation OB The value of s is the standard deviation of e which is a measure of the differences in standard deviations for the two samples OC The value of so is the standard error of the estimate which is a measure of the differences between the observed weights and the weights predicted from the regression equation OD The value of se is the standard error of the estimate which is a measure of the differences in standard deviations for the two samples KC 23

The accompanying technology output was obtained by using the paired data consisting of foot lengths cm and heights cm of a sample of 40 people Along with the paired sample data the technology was also given a foot length of 10 5 cm to be used for predicting height The technology found that there is a linear correlation between height and foot length If someone has a foot length of 10 5 cm what is the single value that is the best predicted height for that person Click the icon to view the technology output The single value that is the best predicted height is Round to the nearest whole number as needed Technology Output The regression equation is Height 54 8 4 21 Foot Length Predictor Constant Foot Length Coef SE Coef 54 78 11 11 4 2136 New Obs 1 S 5 50355 R Sq 73 28 R Sq adj 72 5 Predicted Values for New Observations 4 93 0 000 0 4745 8 88 0 000 Fit SE Fit 99 023 1 795 cm 95 CI 95 217 102 829 Values of Predictors for New Observations 95 PI 87 191 110 855 X ir W lc et pla xpert

Assume that you have paired values consisting of heights in inches and weights in lb from 40 randomly selected men The linear correlation coefficient ris 0 516 Find the value of the coefficient of determination What practical information does the coefficient of determination provide Choose the correct answer below OA The coefficient of determination is 0 734 26 6 of the variation is explained by the linear correlation and 73 4 is explained by other factors B The coefficient of determination is 0 266 26 6 of the variation is explained by the linear correlation and 73 4 is explained by other factors OC The coefficient of determination is 0 266 73 4 of the variation is explained by the linear correlation and 26 6 is explained by other factors OD The coefficient of determination is 0 734 73 4 of the variation is explained by the linear correlation and 26 6 is explained by other factors

A study was conducted to determine whether magnets were effective in treating pain The values represent measurements of pain using the visual analog scale Assume that both samples are independent simple random samples from populations having normal distributions Use a 0 05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets What are the null and alternative hypotheses OA Ho 002 H 0 0 2 OC H 0 0 H 0 0 2 Identify the test statistic F Round to two decimal places as needed B H 0 0 2 H 0 0 2 D H 0 0 H 0 0 n Sham 20 Magnet 20 X S 0 44 1 3 0 49 0 91

A research center poll showed that 78 of people believe that it is morally wrong to not report all income on tax returns What is the probability that someone does not have this belief The probability that someone does not believe that it is morally wrong to not report all income on tax returns is Type an integer or a decimal

the selections independent or dependent If the selections are dependent can they be treated as independent for th adults in a region If a polling organization randomly selects 1235 adults without replacement purposes of calculations Are the selections independent or dependent OA The selections are independent because the selection is done without replacement OB The selections are independent because the sample size is small relative to the population OC The selections are dependent because the sample size is not small relative to the population D The selections are dependent because the selection is done without replacement If the selections are dependent can they be treated as independent for the purposes of calculations OA Yes because the sample size is less than 5 of the population OB No because the sample size is greater than 5 of the population OC Yes because the sample size is greater than 5 of the population OD The selections are independent Sa

The following are the ratings of men by women in an experiment involving speed dating Use the given data to constr a boxplot and identify the 5 number summary 2 0 2 5 3 5 4 0 4 5 4 5 5 5 5 5 5 5 5 5 5 5 6 5 6 5 7 0 7 0 7 0 7 5 8 0 8 5 9 5 The 5 number summary is and Use ascending order Type integers or decimals Do not round Which boxplot below represents the data OA C 0 2 2 4 6 Ratings co 4 6 Ratings 8 00 8 10 10 Q Q O OB O D 0 2 0 2 6 Ratings 4 6 Ratings 00 8 8 10 10 O O

yes years of three government officials when they died in office were 55 44 and 61 Complete parts a through d Part 4 of 4 C Compare the population as to wear the sample ranges Choose the well die vel Tawenimana HW Score 59 76 5 98 of 10 points Points 0 91 of 1 GIIN 06 27 23 9 58 PM Sa OA The population range is equal to the age of the oldest official at the time of death and the mean of the sample ranges is equal to the youngest official at the time death OB The population range is equal to the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death c The population range is not equal to the mean of the sample ranges it is also not equal to the age of the oldest official or age of the youngest official at the time of death OD The population range is equal to the mean of the sample ranges d Do the sample ranges target the value of the population range In general do sample ranges make good estimators of population ranges Why or why not A The sample ranges target the population range therefore sample ranges make good estimators of population ranges OB The sample ranges target the population range therefore sample ranges do not make good estimators of population ranges OC The sample ranges do not target the population range therefore sample ranges make good estimators of population ranges OD The sample ranges do not target the population range therefore sample ranges do not make good estimators of polation

Researchers conducted trials to investigate the effects of color on creativity Subjects with a red background were asked to think of creative uses for a brick other subjects with a blue background were given the same task Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table Higher scores correspond to more creativity The researchers make the claim that blue enhances performance on a creative task Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b Click the icon to view the summary statistics a Use a 0 01 significance level to test the claim that blue enhances performance on a creative task What are the null and alternative hypotheses OA Ho M H Hy H OC Ho H 2P2 H Hy P Response Summary Statistics Background p Blue Red n X S 44 3 79 0 61 3 06 0 95 1 43 OB Ho M 1 H g M OD Ho M 1 H H H X

genetics experiment involves a population of fruit flies consisting of 2 males named Andre and Bob and 2 females named Courtney and Diane Assume that two fruit flies are randomly selected with replacement 1 1 4 Type integers or fractions b Find the mean of the sampling distribution Save 0 5 Round to two decimal places as needed c Is the mean of the sampling distribution from part b equal to the population proportion of males If so does the mean of the sampling distribution of proportions always equal the population proportion OA Yes the sample mean is equal to the population proportion of males These values are always equal because proportion is an unbiased estimator OB No the sample mean is equal to the population proportion of males These values are not always equal because proportion is a biased estimator OC Yes the sample mean is equal to the population proportion of males These values are always equal because proportion is a biased estimator OD No the sample mean is equal to the population proportion of males These values are not always equal because proportion is an unbiased estimator