Statistics Questions

11 Let f x x ax 2 Determine the values of a and b so that f x has a vertical asymptote at x 3 but no x bx 3 other vertical asymptotes

J and K are independent events P J K 0 22 Find P J P J 0 22

To the right are the outcomes that are possible when a couple has three children Refer to that list and find the probability of each event a Among three children there are exactly 2 boys b Among three children there are exactly 3 girls c Among three children there is exactly 1 boy a What is the probability of exactly 2 boys out of three children Type an integer or a simplified fraction 1st 2nd boy boy bo boy boy gir boy girl bo boy girl gir girl boy bo girl boy gir girl girl bo girl girl gir 3r

If a couple were planning to have three children the sample space summarizing the gender outcomes would be bbb bbg bgb bgg gbb gbg ggb ggg a Construct a similar sample space for the possible eye color outcomes using b for blue eyed and g for green eyed of two children b Assuming that the outcomes listed in part a were equally likely find the probability of getting two green eyed children c Find the probability of getting exactly one blue eyed child and one green eyed child a What is the sample space Use a comma to separate answers as needed

Draw a tree diagram for spinning Spinner A two times and then Spinner B one time Use the diagram to find the number of possible outcomes OA RB B R Y X R B R B Spinner A R OB B R B 3 Spinner B 1 3 4 O C Red Blue Yellow Red Blue Yellow Red Blue lud Yellow Red Blue Yellow O D R B Y 2 1 2 1 Red Blue Yellow Ral Blue Yellow Ral Blu Yellow Ral Blu Yellow Rel Bluc Vallow Rol 4 flou Vellem Ral Blue Yellos Clear all 24 34 Vellow Red Blac Yelloww Ral Hlus Vellon Ruf Blac Villes Ral Bla Villim 44 Check

J and K are independent events P J K 0 22 Find P J P J

Giving a test to a group of students the grades and gender are summarized below A C Male 7 17 13 Female 4 12 9 Total 11 29 22 B Total 37 25 62 If one student is chosen at random Find the probability that the student was male 59 67 Find the probability that the student was male AND got a B 45 94 Find the probability that the student was male OR got an C If one student is chosen at random find the probability that the student got a C GIVEN they are mal

Let X represent the full height of a certain species of tree Assume that X has a normal probability distribution with 203 6 ft and o 90 ft You intend to measure a random sample of n 66 trees a What is the mean of the distribution of sample means P ft b What is the standard deviation of the distribution of sample means i e the standard error in estimating the mean ft

O Points 0 of 2 The table provided below shows paired data for the heights of a certain country s presidents and their main opponents in the election campaign Construct a scatterplot Does ther appear to be a correlation Click the icon to view the data table for election heights Construct a scatterplot Choose the correct graph below O A Opponents height 200 O H 160 160 BA O P d 200 President s height OB Opponents height 200 160 160 U Part 1 of 2 200 President s height Q O C 200 160 200 160 President s height O D 200 A 160 E ala 5 A OR h P O 160 200 President s height Save

Minh a psychology student kept a record of how much time she spent studying for each of her 20 point psychology quizzes and her score on each quiz Hours Spent Studying 0 50 0 75 1 00 1 25 1 50 1 50 1 75 2 00 Quiz Score 10 12 13 14 15 18 18 19 Chat we can staller urayram OA Quiz Score 20 Quiz Score OC A 0 0 2 Hours Spent Studying 20 0 0 2 Hours Spent Studying OB Quiz Score Quiz Score 201 0 0 2 Hours Spent Studying D 20 0 0 Hours Spent Studying G Q d What might Minh conclude from the scatter diagram OA Quiz score increases as she spent more hours studying OB Quiz score does not depend upon the hours spent for studying OC Quiz score decreases as she spent more hours studying

The table shows the worldwide box office in billions of dollars for the movie industry during the years shown Year 2000 2002 2004 2006 2008 Box office in billions of dollars 22 1 24 5 25 7 26 8 28 5 UP w year 2000 the UNG DUA Vice was to a B The worldwide box office was equal to 2008 28 5 billion OC In the year 2008 the worldwide box office was 28 5 billion more than the previous years D In the year 2008 the worldwide box office was 28 5 billion c Create a scatter diagram of the paired data Choose the correct scatter diagram below OA OB Box Office 30 Bax Office 0 1999 OC 30 0 1999 Year 2009 2009 Q 5 Box Office 30 O D Box Office 0 1999 30 0 1999 Year Year 2009 2009 Q OF Q Q

The population proportion of success is 21 and the intended sample size is n 11 Before drawing a sample from the population you first want to describe the expected sampling distribution for the sample proportion Give answers in decimal format as opposed to fractions or percentages Give the mean for the distribution of sample proportions H Give the standard deviation for the distribution of sample proportions

When you take samples from a population and compute a proportion from each one you can consider the distribution of those proportions This is called the sampling distribution for the population proportion The Central Limit Theorem tells us that the sampling distribution for the population proportion is with the Select an answer as its Select an answer O Select an answer

Suppose the mean starting salary for nurses is 66 239 nationally The standard deviation is approximately 10 660 The starting salary is not normally distributed but it is mound shaped A sample of 40 starting salaries for nurses is taken State the random variable O The standard deviation of starting salaries of nurses The mean starting salary of a nurse Starting salary for a nurse What is the mean of the sample mean H

The amount of time to complete a physical activity in a PE class is approximately normally distributed with a mean of 35 8 seconds and a standard deviation of 5 7 seconds a What is the probability that a randomly chosen student completes the activity in less than 30 5 seconds b What is the probability that a randomly chosen student completes the activity in more than 42 2 seconds

The actual volumes of quart size jars of Hellmann s mayonnaise are uniformly distributed from 31 4 t 32 57 fluid ounces Find the average volume of a quart size jar of Hellmann s in fluid ounces NOTE There are 32 fluid ounces in a quart 32 102 31 903 31 950 32 020 31 985 31 868 32 067

A local unemployment agency keeps track of the number of new claims filed each day Based on the data collected it determines the following discrete probability distribution where X is the number of claims filed each day X number of claims 0 1 2 3 4 P X 0 13 0 13 0 46 0 09 Use this discrete probability distribution to answer each question Give all answers as exact decimals Do not round a What is the probability that there are no claims on a randomly selected day b What is the probability that the agency receives at least 2 claims on a randomly selected day

You have a really annoying stapler that seems to randomly jam On any given attempt to staple it seems to independently jam 17 2 of the time a Out of 280 papers stapled what is the probability that your stapler will jam 41 times or fewer b Find the mean and standard deviation for the number of jammed staples out of 280 attempts Mean Standard Deviation

Determine if the following scenario is a binomial experiment If it is not binomial then select all of the reasons why Brand A has a history of recalling 27 of their products An employee at Walmart is going through a list of 54 recalls and records the number of products being recalled by Brand A The variable is not discrete There is not a fixed number of trials There are more than two outcomes The trials are not independent O The probability of success is not the same for each trial O All of the conditions for being a binomial experiement are met i e this is a binomial experiment

A CBS News poll conducted June 10 and 11 2006 among a nationwide random sample of 651 adults asked those adults about their party affiliation Democrat Republican or none and their opinion of how the US economy was changing getting better getting worse or about the same The results are shown in the table below Republican Democrat none Express your answers as a decimal and round to the nearest 0 001 in other words type 0 123 not 12 3 or 0 123456 If we randomly select one of the adults who participated in this study compute P Republican P better better same worse 38 104 44 12 87 137 21 90 118 Dibetter Republican

A student kept a record of how much time he spent studying for each of his 20 point health quizzes and his score on each quiz Complete parts a through d below Hours Spent Studying 0 50 0 75 1 00 Quiz Score 1 75 1 75 2 00 9 12 14 18 19 20 A A The student has to study for 1 25 hours to earn a quiz score of 14 OB When the student studies for 1 25 hours his quiz score will be 14 C When the student studied for 1 25 hours his quiz score was 14 c Create a scatter diagram of the paired data Choose the correct diagram below Hours spent studying 2 00 1 50 1 00 0 50 0 00 0 5 10 15 20 Quiz score Q o o 1 25 14 5 1 50 15 OB Quiz score 20 15 10 53 0 0 00 1 00 Hours spent studying 2 00 OC 20 15 10 5 3 07 0 00 1 00 Hours spent studying 2 00

Complete the following probability distribution table X 21 12 42 64 66 69 P X 0 22 0 13 0 15 0 13 0 13

An appliance dealer sells three different models of upright freezers having 13 6 16 0 and 19 3 cubic feet of storage space Consider the random variable x Amount of storage space purchased by the next customer to buy a freezer Suppose that x has the following probability distribution Hx ox X 13 6 16 0 19 3 P x 0 2 a Calculate the mean and standard deviation of x in cubic feet Hint See Example 6 15 Round your standard deviation to four decimal places X cubic ft X cubic ft 0 5 0 3 MY NOTES b Give an interpretation of the mean and standard deviation of x in the context of observing the outcomes of many purchases The mean represents the long run average number of freezers sold by this particular appliance dealer The standard deviation represents a typical deviation in how many freezers purchased deviates from the mean The mean represents the long run average distribution of freezers sold by this particular appliance dealer The standard deviation represents a typical deviation in how much the distribution in freezers purchased deviates from the mean The mean represents the long run average type of freezer sold by this particular appliance dealer The standard deviation represents a typical deviation in what type of freezer purchased deviates from the mean The mean represents the long run average cost of freezers sold by this particular appliance dealer The standard deviation r presents a typical deviation in how much is spent on freezers purchased deviates from the mean The mean represents the long run average storage space of freezers sold by this particular appliance dealer The standard deviation represents a typical deviation in how much the storage space in freezers purchased deviates from the mean X

6 In a survey 12 people were asked how much they spent on their child s last birthday gift The results appeared bell shaped with a mean of 87 and a standard deviation of 4 a 1 pt Construct a confidence interval at a 95 confidence level You do not need to list definitions or assumption checks Round solutions to the third decimal place b 2 pts State a real world interpretation of this interval

Consider n independent trials of an experiment in which each trial has two possible outcomes success or failure The probability of a success on each trial is p and the probability of a failure is q 1 p In this context the term Ckpkq k in the expansion of p q gives the probability of k successes in the n trials of the experiment The probability of a baseball player getting a hit during any given time at bat is 1 4 To find the probability that the player gets two hits during the next 11 times at bat evaluate the term shown below in the expansion of 1 4 3 4 11 Round your answer to four decimal places 9 11 C 1 4 3 4

OBFW Publishers A media report claims that 50 of U S teens with smartphones feel addicted to their devices A skeptical researcher believes that this figure is too high She decides to test the claim by taking a random sample of 100 U S teens who have smartphones Only 40 of the teens in the sample feel addicted to their devices Does this result give convincing evidence that the media report s 50 claim is too high To find out we want to perform a simulation to estimate the probability of getting 40 or fewer teens who feel addicted to their devices in a random sample of size 100 from a very large population of teens with smartphones in which 50 feel addicted to their devices Let 1 feels addicted and 2 doesn t feel addicted Use a random number generator to produce 100 random integers from 1 to 2 Record the number of I s in the simulated random sample Repeat this process many many times Find the percent of trials on which the number of 1 s was 40 or less Does the problem describe a valid simulation design Justify your answer O No it does not describe a valid simulation design The simulation should let 0 3 feels addicted and 4 9 doesn t feel addicted O No it does not describe a valid simulation design It does not specify that you should ignore repeating numbers when choosing integers from the random number generator O No it does not describe a valid simulation design It does not specify how many times to repeat the simulation Yes it describes a valid simulation design By letting 1 feels addicted and 2 doesn t feel addicted the simulation would model the claim that 50 of U S teens with smartphones would feel addicted to their devices No it does not describe a valid simulation design The simulation should let 0 5 feels addicted and 6 9 doesn t feel addicted

A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low fat diet To check that the random assignment did produce comparable groups we can compare the two groups at the start of the study Asked if there is a family history of breast cancer 840 of the 6318 women in the low fat group and 590 of the 5417 women in the control group said Yes If the random assignment worked well there should not be a significant difference in the proportions with a family history of breast cancer How significant is the observed difference State Is there evidence of a difference in the proportion of women with a family history of breast cancer between the treatment and control groups Plan Let p be the proportion for the treatment group and p2 the proportion for the control group State the hypotheses for your test Ho P P2 Ha P1 P2 Solve Give the value of the test statistic Use the calculator Select an answer What is the P value for the test What do you conclude O There is evidence that the two proportions differ at the 0 10 significance level The difference between the sample proportions is not significant at the 0 10 level The data prove that the null hypothesis is true That is the randomization worked

Only about 10 of all people can wiggle their ears Is this percent higher for millionaires Of the 334 millionaires surveyed 37 could wiggle their ears What can be concluded at the a 0 10 level of significance a For this study we should use z test for a population proportion OB b The null and alternative hypotheses would be Ho PE B O OT 8 B O H Pv V 0 10 please enter a decimal 0 10 Please enter a decimal c The test statistic z 1 729 x please show your answer to 3 decimal places

You wish to test the following claim Ha at a significance level of a 0 10 Ho P P2 Ha P1 P2 You obtain 28 5 successes in a sample of size n 228 from the first population You obtain 42 4 successes in a sample of size n 794 from the second population Calculator tip test statistic What is the p value for this sample p value The p value is O less than or equal to a Ogreater than a This test statistic leads to a decision to O reject the null accept the null O fail to reject the null As such the final conclusion is that O There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion O There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion O The sample data support the claim that the first population proportion is not equal to the second population proprtion O There is not sufficient sample evidence to support the claim that the first population proportion is not equal to the second population proprtion

51 of students entering four year colleges receive a degree within six years Is this percent different from for students who play intramural sports 108 of the 216 students who played intramural sports received a degree within six years What can be concluded at the level of significance of a 0 05 a For this study we should use z test for a population proportion OF b The null and alternative hypotheses would be Ho p 8 f 8 0T H pv OF B OB 8 c The test statistic zv Z OF d The p value e The p value is a 0 51 please enter a decimal 0 51 Please enter a decimal please show your answer to 3 decimal places Please show your answer to 4 decimal places

The US Department of Energy reported that 50 of homes in the USA were heated by natural gas A random sample of 335 homes in Oregon found that 130 were heated by natural gas Test the claim that proportion of homes in Oregon that were heated by natural gas is different from the US reported proportion Use a 10 significance level Give answers accurate to at least 3 decimal places What are the correct hypotheses Select the correct symbols and use decimal values not percentages Ho P H P Or V O 0 50 Test Statistic 0 50 Based on the hypotheses find the following OPT

5 1 pt A population is normally distributed with a standard deviation of 2 6 From a sample of size 45 you find a sample mean of 61 Find a 95 confidence interval for the mean of this population You do not need to list definitions or assumption checks Round solutions to the third decimal place

4 A college president commissioned a study to find the proportion of students enrolled at her college that binge drink In the study 150 out of 320 students admitted to having engaged in binge drinking a 1 pt Find a 99 confidence interval for the proportion of students who engage in binge drinking at this school You do not need to list definitions or assumption checks Round solutions to the third decimal place b 2 pts State a real world interpretation of this interval

2 1 pt Suppose you compute a 95 confidence interval What will happen to the confidence interval if you increase the confidence level to 99

1 1 pt Suppose you compute a confidence interval with a sample size of 40 What will happen to the confidence interval if the sample size increases to 75

3 1 pt Rewrite the confidence interval 43 4 in interval form

1 Visitors to the Monterey Bay Aquarium The Monterey Bay Aquarium founded in 1984 is situated on the beautiful coast of Monterey Bay in the his toric Cannery Row district In 1985 the aquarium began a survey program that involved randomly sampling visitors as they exit for the day The survey in cluded visitor demographic information use of social media and opinions on their aquarium visit Here is a comparison of the age distribution of Hispanic and Caucasian visitors in 2015 AGEDIST Age Category 18 to 24 25 to 34 35 to 44 45 to 54 55 and over Caucasian 785 1413 1027 859 1255 Hispanic 586 938 594 180 160 a What percent of Caucasian visitors are in each age category What percent of Hispanic visitors are in each category Each column should add to 100 up to roundoff error These are the conditional distributions of age category given ethnic group b Make a bar graph that compares the two conditional distributions What are the most important differences in age between the two ethnic

Which of the following is NOT an assumption or condition for a hypothesis test for two means Randomization Assumption Independence Assumption Success Failure Condition Is n big enough

A newsgroup is interested in constructing a 95 confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative Of the 593 randomly selected Texans surveyed 362 were in favor of the initiative and of the 539 randomly selected New Yorkers surveyed 452 were in favor of the initiative a With 95 confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between round to 3 decimal places and round to 3 decimal places b If many groups of 593 randomly selected Texans and 539 randomly selected New Yorkers were surveyed then a different confidence interval would be produced from each group About percent of these confidence intervals will contain the true population proportion of the difference in the proportions of Texans and New Yorkers who favor a new Green initiative and about percent will not contain the true population difference in proportions

Two samples are taken with the following numbers of successes and sample sizes 71 33 72 38 n 90 n 64 Find a 97 confidence interval round answers to the nearest thousandth P1 P2

Cereal for Breakfast A parent claims that kids eat cereal for breakfast more often than adults A statistics loving friend of the parent does some internet research and finds the following polling data Of 80 kids polled 60 of them say cereal is their most common breakfast Of 55 adults polled 22 of them say cereal is their most common breakfast Test the parent s claim using these data a Select the correct null and alternative hypotheses O Ho Pkids Padults Ha Pkids Padults O Ho Pkids Padults Ha Pkids Padults O Ho Pkids Padults Ha Pkids Padults b Find the p value round to three significant figures c Write the final conclusion using everyday language O There is not sufficient evidence to support the parent s claim O There is sufficient evidence to support the parent s claim O There is sufficient evidence to reject the parent s claim O There is not sufficient evidence to reject the parent s claim

Sample A has 796 number of successes from a sample size of 805 Sample B has 794 number of successes from a sample size of 815 Find the 95 confidence interval for the difference between the two sample proportions P1 P2 Use a calculator

In a survey funded by the UW school of medicine 750 of 1 000 adult Seattle residents said they did not believe they could contract a sexually transmitted infection STI and 893 of 1 123 Denver residents said they did not believe they could contract an STI Construct a 95 confidence interval of the difference in proportions of Seattle and Denver residents who do not believe they could contract a STI Use a z score of 1 96 for your computations O 0809 0095 O 0809 0095 O 0809 0095 O 0095 0809

A CCBC professor claims that there is a difference between the mean class score of statistics day students on Test 3 and statistics evening students on the Test 3 The professor takes random samples from each group of students The summary is shown in the table below Day Evening n 49 36 Ho D E HANDHE What are the correct hypothesis statements for this situation Ho MD ME HANDE O Ho PD PE HA PD PE x 76 80 H HD NE HAND ME S 13 10

5 15 Saving Birds from Windows Many birds are injured or killed by flying into windows It appears that birds don t see windows Can tilting windows down so that they reflect earth rather than sky reduce bird strikes Place six win dows at the edge of a woods two vertical two tilted 20 degrees and two tilted 40 degrees During the next four months there were 53 bird strikes 31 on the vertical windows 14 on the 20 degree windows and 8 on the 40 degree windows If the tilt has no effect we expect strikes on windows with all three tilts to have equal probability Test this null hypothesis What do you conclude

A researcher has developed a new drug designed to reduce blood pressure In an experiment 21 subjects wer assigned randomly to the treatment group and received the new experimental drug The other 23 subjects were assigned to the control group and received a standard well known treatment After a suitable period the reduction in blood pressure for each subject was recorded A summary of these data is n x S Treatment group new drug Control group old drug 21 23 23 48 18 52 8 01 7 15 Without using software how would you estimate the number of degrees of freedom for this problem O A Use the smaller value 21 chosen from the two options 21 and 23 O B Use the larger value 23 chosen from the two options 21 and 23 O C Use the smaller value 20 chosen from the two options 20 and 22 D Use the larger value 22 chosen from the two options 20 and 22

A veterinarian was studying suspected causes of enteroliths concretelike balls in the colons of horses She suspected that a diet of mostly alfalfa could be a cause In a study conducted at a veterinary research facility she examined the records of 62 horses with enteroliths cases and compared them with the records of 75 horses free of enteroliths controls To assess the conjecture that horses that are fed primarily alfalfa are m prone to getting enteroliths she should test the following hypothesis where O A Pcase Pcontrol 0 4507 vs Ha Pcase Pcontrol 0 4507 OB Ho Pcase Pcontrol 0 vs Ha Pcase Pcontrol 0 OC Ho Peace control 0 vs Ha Pease Pcontrol 0 OD Ho Praze control 0 4507 vs Ha Pcare control 0 4507

A candidate for one of Ohio s two U S Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state A random sample of 2000 registered voters in the northern half of the state is selected of which 1062 support the candidate Additionally a random sample of 2000 registered voters in the southern half of the state is selected of which 900 support the candidate A 95 confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is O A 0 037 to 0 119 OB 0 050 to 0 112 OC 0 040 to 0 122 O D 0 035 to 0 127

Students conducted a survey and found out that 36 of their peers on campus had tattoos but only 4 of their peers were smokers The standard error of of tattooed students in the 100 student sample is p O A 4 OB 5 O C 6 OD It is not possible to tell from the information provided

Students conducted a survey and found out that 36 of their peers on campus had tattoos but only 4 of their peers were smokers If 100 students were surveyed can these students use the Normal approximation to study the proportion of students in the population who have tattoos O A no because either np or n 1 p are greater than 15 O B yes because both np and n 1 p are greater than 15 O C yes because both np and n 1 p are less than 15 O D no because either np or n 1 p are less than 15