Statistics Questions

Over the years the mean customer satisfaction rating at a local restaurant has been 80 The restaurant was recently remodeled and now the management claims the mean customer rating is not equal to 80 In a sample of 54 customers chosen at random the mean customer rating is 73 6 Assume that the population standard deviation of customer ratings is 21 1 Is there enough evidence to support the claim that the mean customer rating is different from so Perform a hypothesis test using the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H H O H 0 b Perform a Z test and find the p value Here is some information to help you with your z test The value of the test statistic is given by Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the test statistic Round to 3 decimal places Step 3 Shade the area represented by the p value x 0 n Step 4 Enter the p value Round to 3 decimal places 102 The p value is two times the area under the curve to the left of the value of the test statistic 03 02 0 1 Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal to 80 Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal to 80 HX Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal to 80 Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal to 80 O O OSO 0 O 020 0 0 00 X c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the management 4 S X X

A sample of computer tablet batteries has a mean battery life of 28 months and standard deviation of 4 months What is the lifespan of batteries that are within the given standard deviations of the mean Use Notes Try it 1 1 1 standard deviation 2 2 standard deviations 24 32 20 36 Find the mean and standard deviation of the following sample of data Ex 2 4 6 49 67 58 55 62 70 52 65 60 58 28 12 15 17 22 25 19 23 15 26 5 4 0 2 7 3 0 3 3 3 3 3 7 3 7 4 0 3 0 2 3 The variance is o 15 7 The table shows sample data of how many minutes students spend on homework each night Ex 4 The mean of the data is x 225 The standard deviation is S 2 X 8 1 3 3 standard deviations 16 40 8 1 2 Last Season 10 3 20 27 35 17 20 13 17 This Season 23 17 28 16 23 16 16 10 13 90 75 60 85 65 80 70 75 8 The table shows the points scored by a community football team during two seasons Use the mean and standard deviation to determine during which season the team scored more consistently

The data below show sport preference and age of participant from a random sample of members of a sports club Is there evidence to suggest that they are related Frequencies of Sport Preference and Age Tennis Basketball 18 25 84 76 26 30 96 86 87 31 40 87 71 62 Over 40 56 57 61 What can be concluded at the a 0 01 significance level Swimming 96 a What is the correct statistical test to use Goodness of Fit Independence Homogeneity Paired t test b What are the null and alternative hypotheses Ho H Age and sport preference are dependent The age distribution is not the same for each sport Age and sport preference are independent The age distribution is the same for each sport Age and sport preference are independent Age and sport preference are dependent The age distribution is not the same for each sport The age distribution is the same for each sport c The test statistic for this data d The p value for this sample Please show your answer to three decimal places Please show your answer to four decimal places

Greenspan National Park hikes during their visit is 30 kilometers The park recently closed its shuttle system which used to transport hikers to many of the park s most popular hiking trails Because of this an administrator at the park suspects the mean distance is now less than 30 kilometers The administrator chooses a random sample of 45 visitors The mean distance hiked for the sample is 28 5 kilometers Assume the population standard deviation is 9 9 kilometers Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers Perform a hypothesis test using the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis H Ho H 0 given by z z b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test x G Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed 20 10 is the value that cuts off an area of 0 10 in the right tail The test statistic has a normal distribution and the value is Step 2 Enter the critical value s Round to 3 decimal places Step 3 Enter the test statistic Round to 3 decimal places 03 02 01 Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 30 kilometers Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to conclude that the mean distance hiked by each visitor is now less than 30 kilometers Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 30 kilometers O O OSO O 020 Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to conclude that the mean distance hiked by each visitor is now less X x c Based on your answer to part b choose what the researcher can conclude at the 0 10 level of significance 0 0 X S

Migraine and Acupuncture A migraine is a particularly painful type of headache which patients sometimes wish to treat with acupuncture To determine whether acupuncture relieves migraine pain researchers conducted a randomized controlled study where 161 patients diagnosed with migraine headaches were randomly assigned to one of two groups treatment or control 77 patients in the treatment group received acupuncture that is specifically designed to treat migraines 84 patients in the control group received placebo acupuncture needle insertion at non acupoint locations 24 hours after patients received acupuncture they were asked if they were pain free Results are summarized in the contingency table below Test to see if migraine pain relief is dependent on receiving acupuncture Use a 0 05 Pain Free Yes Pain Free No 15 62 6 78 21 140 Treatment Control Total a What is the correct null hypothesis Ho Migraine pain relief is independent on receiving acupuncture Ho P1 P2 P3 P4 Ho P1 P2 P3 P4 Ho Migraine pain relief is dependent on receiving acupuncture Total 77 84 161 b Fill in the expected values round answers to at least 2 decimal places Expected Values Pain Free Yes Pain Free No Treatment Control Answers show on last attempt Treatment Control Pain Free Yes Pain Free No c Find the test statistic round answer to at least 3 decimal places d What is the p value Round answer to at least 3 decimal places

A researcher is interested in investigating whether living situation and pet ownership are dependent The table below shows the results of a survey Frequencies of Living Situation and Pet Single Family Dog 64 95 Cat 96 87 Various 44 44 None 50 44 What can be concluded at the 0 10 significance level H Couple 83 94 a What is the correct statistical test to use Homogeneity Goodness of Fit Paired t test Independence b What are the null and alternative hypotheses Ho 56 38 The distribution of pets is the same for each living situation The distribution of pets is not the same for each living situation d The p value for this sample Pet ownership and living situation are dependent Pet ownership and living situation are independent Pet ownership and living situation are dependent The distribution of pets is not the same for each living situation The distribution of pets is the same for each living situation Pet ownership and living situation are independent c The test statistic for this data Please show your answer to three decimal places Please show your answer to four decimal places

Based on advancements in drug therapy a pharmaceutical company is developing Resithan a new treatment for depression A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug Exemor A random sample of 573 depressed individuals is selected and treated with Resithan and 293 find relief from their depression A random sample of 408 depressed individuals is independently selected from the first sample and treated with Exemor and 197 find relief from their depression Based on the medical researcher s study can we conclude at the 0 05 level of significance that the proportion p of all depressed individuals taking Resithan who find relief from depression is greater than the proportion all depressed individuals taking Exemor who find relief from depression Perform a one tailed test Then complete the parts below a State the null hypothesis H and the alternative hypothesis H H 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 Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below If necessary consult a list of formulas d Find the p value Round to three or more decimal places e Can we conclude that the proportion of depressed individuals taking Resithan who find relief is greater than the proportion taking Exemor who find relief Yer No 3 x X 5 a X S 2 O O p 0 0 OSO 020 Q olo O O P2 of

Do men and women select different breakfasts The breakfasts ordered by randomly selected men and women at a popular breakfast place are shown below Frequencies of Breakfasts for Men and Women French Toast Pancakes Waffles 88 93 84 110 Men Women What can be concluded at the a 0 01 significance level a What is the correct statistical test to use Paired t test H 54 67 Independence Homogeneity Goodness of Fit b What are the null and alternative hypotheses Ho Omelets 74 54 Breakfast ordered and gender are independent Breakfast ordered and gender are dependent The distribution of breakfast ordered for men is the same as it is for women The distribution of breakfast ordered for men is not the same as it is for women d The p value for this sample The distribution of breakfast ordered for men is not the same as it is for women Breakfast ordered and gender are dependent Breakfast ordered and gender are independent The distribution of breakfast ordered for men is the same as it is for women c The test statistic for this data Please show your answer to three decimal places Please show your answer to four decimal places

With a new style of physical therapy a researcher claims that the mean recovery time is less than 13 weeks In a random sample of 32 knee surgery patients who practiced this new physical therapy the mean recovery time is 12 8 weeks Assume that the population standard deviation of recovery times is known to be 1 1 weeks Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks Perform a hypothesis test using the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis H H b Perform a Z test and find the p value Here is some information to help you with your Z test The value of the test statistic is given by 0 n Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the test statistic Round to 3 decimal places Step 3 Shade the area represented by the p value Step 4 Enter the p value Round to 3 decimal places 03 The p value is the area under the curve to the left of the value of the test statistic 02 01 O Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks H Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks 0 0 0 0 0 0 X 09 020 0 0 X c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the claim made by the researcher X 00 X S S S

An endangered species of birds has a current population of 4200 It is estimated that the population decreases by 4 8 each year a Write an equation to estimate y the number of birds n years from now b Estimate the number of birds 12 years from now ALT 510 PC or ALT FN F10 Mac

restaurant has been 79 The restaurant was recently remodeled and now the management claims the mean customer rating is not equal to 79 In a sample of 51 customers chosen at random the mean customer rating is 81 4 Assume that the population standard deviation of customer ratings is 7 6 Is there enough evidence to support the claim that the mean customer rating is different from 79 Perform a hypothesis test using the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis H Ho O H 0 given by 23 b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test x G n Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the critical value s Round to 3 decimal places 70 05 is the value that cuts off an area of 0 0s in the right tail The test statistic has a normal distribution and the value is Step 3 Enter the test statistic Round to 3 decimal places 03 02 01 Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal 79 Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal 79 O O Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal 79 020 Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal 79 X X c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the claim made by the management OSO O O X 0 0 S

by passengers on its flights in order to evaluate the appropriateness of their overweight fees Recently a random sample of 249 items checked on English Air flights to North America contained 52 overweight items and an independent random sample of 272 items checked on English Air flights within Europe contained 32 overweight items Based on these samples can we conclude at the 0 10 level of significance that there is a difference between the proportion p of all items on English Air flights to North America that are overweight and the proportion p of all items on English Air flights within Europe that are overweight P2 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 parts below 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 two critical values at the 0 10 level of significance Round to three or more decimal places and e Can we conclude that the proportion of items that are overweight is different between the two types of English Air flights QYes No 3 X 4 0 0 X O S 2 O O P P OSO 020 S alo 0 0

Suppose that in Franklin county 69 of households have a dog 45 of households have a dog and a cat You randomly select a household that has a dog What is the probability that it also has a cat Show your work here

Background Morris Saldov conducted a study in Eastern and Central Newfoundland in 1988 to examine public attitudes towards social spending In particular the study tried to determine if knowing someone on public assistance yes no affected one s views on social spending too little about right too much The data from the study is summarized in the table below Too little About right Too much Total Yes No Total 38 6 44 16 13 29 10 9 19 64 28 92 Source Morris Saldov Public Attitudes to Social Spending in Newfoundland Canadian Review of Social Policy 26 November 1990 pages 10 14 Directions Conduct a chi square test for independence to determine if the association between knowing someone on public assistance and views on social spending is statistically significant 1 Choose the correct null and alternative hypotheses Ho There is an association between knowing someone on public assistance and views on social spending Ha There is no association between knowing someone on public assistance and views on social spending Ho There is no association between knowing someone on public assistance and views on social spending Ha There is an association between knowing someone on public assistance and views on social spending 2 Complete the following table of expected counts under the assumption that the null hypothesis is true Round your answers to 1 decimal place Yes Too little About right Too much No 3 Use appropriate technology to compute the value of the test statistic rounded to 2 decimal places and the P value rounded to 3 decimal places P value

Match the linear correlation coefficients to the scatterplots T 0 960 T 1 000 Select an answer Select an answer T 0 966 r 0 857 Select an answer Select an answer Q T 0 883 T 0 385 Select an answer Select an answer Q Q T 0 437 r 1 000 Select an answer Select an answer Q

minutes for its customers Recently the restaurant added several very popular dishes back to their menu Due to this the manager suspects the wait time has increased He takes a random sample of 41 customers The mean wait time for the sample is 11 3 minutes Assume the population standard deviation for the wait times is known to be 2 8 minutes Can the manager conclude that the mean wait time is now greater than 10 minutes Perform a hypothesis test using the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H Ho H 0 given by Standard Normal Distribution b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the critical value s Round to 3 decimal places Step 3 Enter the test statistic Round to 3 decimal places U 70 05 is the value that cuts off an area of 0 0s in the right tail The test statistic has a normal distribution and the value is x u n 03 02 aut Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to conclude that the mean wait time is now greater than 10 minutes LI Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to conclude that the mean wait time is now greater than 10 minutes O Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to conclude that the mean wait time is now greater than 10 minutes 020 Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to conclude that the mean wait time is now greater than 10 minutes X X Oso O 0 c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the chain of restaurants 0 0 0 0 5 5 BEI M

Chest inches 26 45 54 49 35 41 41 a Construct a scatterplot b Compute and plot the least squares regression line Enter the equation in y mx b form Round to 3 decimal places if needed Slope Weight pounds c What is the slope of the least squares regression line including units Interpret the meaning of the slope in this situation Interpretation 210 394 416 308 266 200 282 1 Units Select an answer Select an answer d Predict the weight of a bear with chest size 30 inches

developing Resithan a new treatment for depression A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug Exemor A random sample of 520 depressed individuals is selected and treated with Resithan and 187 find relief from their depression A random sample of 435 depressed individuals is independently selected from the first sample and treated with Exemor and 131 find relief from their depression Based on the medical researcher s study can we conclude at the 0 01 level of significance that the proportion p of all depressed individuals taking Resithan who find relief from depression is greater than the proportion of all depressed individuals taking Exemor who find relief from depression Perform a one tailed test Then complete the parts below P2 Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below 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 proportion of depressed individuals taking Resithan who find relief is greater than the proportion taking Exemor who find relief OYes No H Ix 4 O S X 00 0 0 OSO P 00 020 O O 0 0

Consider the above code Which of the following explanations best describes what the code does Compute the total number of food items Compute the total number of orders for each food item Compute the total number of orders Compute the total number of food items for each order

What is the storage mode for any given factor vector character O logical O factor numeric

Will tapply throw an error if the INDEX argument is not a factor vector O Yes No

Can factors have ordered levels No O Yes

Are the number of levels of a factor independent of the length of the factor O No Yes

What is the storage mode for the levels of any given factor vector O character logical O factor numeric

Which type of data are factors generally used to represent O Categorical O Discrete O Continuous

For a certain knee surgery a mean recovery time of 11 weeks is typical With a new style of physical therapy a researcher claims that the mean recovery time is less than 11 weeks In a random sample of 37 knee surgery patients who practiced this new physical therapy the mean recovery time is 10 6 weeks Assume that the population standard deviation of recovery times is known to be 2 1 weeks Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 11 weeks Perform a hypothesis test using the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H Ho H 0 given by 7 b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test 0 n Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two talled 0 05 is the value that cuts off an area of 0 05 in the right tail The test statistic has a normal distribution and the value is Step 2 Enter the critical value s Round to 3 decimal places Step 3 Enter the test statistic Round to 3 decimal places 0 3 02 0 1 Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 11 weeks H Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 11 weeks O O Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 11 weeks Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean recovery time of patients who X 020 0 0 0 0 X c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the researcher OSO O X S E E

CQ1 Suppose Y is a random variable from under a Gaussian distribution with mean 21 and standard deviation of 5 5 and X is a random variable from under a Gaussian distribution with mean 5 and standard deviation of 1 Is this information alone sufficient to calculate the linear correlation between X and Y

state To see what sorts of people are visiting this new attraction a survey was done at this year s state fair It was found that among a random sample of 73 couples at the fair with their children 47 had visited the new miniature golf course and among an independently chosen random sample of 76 couples at the fair on a date without children 35 had visited the miniature golf course Based on these samples can we conclude at the 0 05 level of significance that the proportion p of all couples attending the fair with their children who visited the miniature golf course is different from the proportion P of all couples attending the fair on a date who visited the miniature golf course 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 parts below If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H H 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 proportion of couples visiting the miniature golf course is different between the two populations OYes No H X 5 O S X P 8 olo 0 0 OSO 020 D 0 0 0 0 0

restaurant has been 80 The restaurant was recently remodeled and now the management claims the mean customer rating is not equal to 80 In a sample of 54 customers chosen at random the mean customer rating is 88 4 Assume that the population standard deviation of customer ratings is 21 1 Is there enough evidence to support the claim that the mean customer rating is different from so Perform a hypothesis test using the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H Ho H 0 given by Z b Perform a hypothesis test The test statistic has a normal distribution so the test is a z test Here is some other information to help you with your test G Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the critical value s Round to 3 decimal places is the value that cuts off an area of 0 025 in the right tail The test statistic has a normal distribution and the value is 20 025 Step 3 Enter the test statistic Round to 3 decimal places 03 02 11 Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal 80 Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal 80 O O Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean customer rating is not equal 80 Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean customer rating is not equal 80 X 020 0 0 0 0 x OSO O O c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the management X S X S

3 Kakashi deposits 2400 into Leaf s National Bank His account offers an annual interest rate of 3 6 a Find Kakashi s bank balance after 7 years if interest is compounded annually 1x per year b Find Kakashi s bank balance after 7 years if interest is compounded daily 365 00000000 100000000 assume

6 The Half life of a radioactive substance is 30 years and you start with 3mg of substance How much is present after 96 years 7 Your car needs repairs and the cost is as follows there is a fixed 250 for parts and 75 per hour for labor a How much will it cost if your car takes 18 hours to repair b Write a linear function that describes the situation Clearly identify all variables used c If you paid 700 to fix the car how many hours of work did they perform on the vehicle

6 6 Fair Die Toss a fair six sided die The probability density func tion pdf in table form is given Make a graph of the pdf for the die Number of Spots Probability 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6

Profit x 10 000 50 4000 3000 2000 1000 0 10000 From this information we see that 20000 Sales x 10 000 30000 there is one very influential observation in the data profits can be accurately predicted from sales All of the answer options are correct there is a clear error because profits cannot be negative 40000

E Frequent food questionnaires FFQ are a simple way to obtain information on the foods that individuals consume by asking them questions about typical amounts of food consumed in a da a week or a month A more accurate picture can be gained by obtaining a detailed food diary DR for several days that are randomly chosen over a certain time period The data obtained from a frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire The data below are for seven individuals who participated in such a study on alcohol consumption DR FFQ 8 26 1 68 0 83 0 20 13 25 11 16 7 49 7 18 12 84 1 76 0 22 66 33 The correlation for these data is 91 94 0 89 86

3 1 point A sociologist studying first year undergraduates at a major university carried out a survey asking among other questions how often students went out per week how many hours they studied per day and how many hours they slept at night Students will often overstate the number of hours studied because they do not want to admit to not studying enough This type of distortion is called under coverage bias nonresponse bias OOOC response bias false answer

1 point A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths stones that form in the colon of horses and diet They decided to conduct a survey of the feeding practices for horses in the hospital s state They created a survey questionnaire and administered it to the owners of every fifth horse being treated at the hospital The sample is a simple random sample Dal a convenience sample a volunteer sample a stratified random sample 0000

1 point The average age of residents in a large residential retirement community is 69 years with standard deviation 9 years A simple random sample of 100 residents is to be selected and the sample mean age x of these residents is to be computed The probability that the average age x of the 100 residents selected is less than 69 15 years is 0 195 OO 0 805 0 043 0 568

35 1 point For this density curve the mean is 0 5 0 4 0 3 0 2 0 1 0 0 0000 0 equal to the median less than the median 2 greater than the median not possible to determine from the information given 3 4

1 point The exam scores out of 100 points for all students taking an introductory statistics course are used to construct the following boxplot Exam Score 00 0 100 80 09 40 20 0 If each person increased his or her score by 5 points then the third quartile would increase by 5 points All of the answer options are correct Time Remaining the median score would increase by 5 points the interquartile range would remain unchanged

1 point Suppose that we have two pyramid shaped 4 sided dice with the faces numbered 1 through 4 Suppose that the two dice are rolled and the numbers showing on bottom are added W the probability that this sum is greater than 4 Suggestion Draw a picture of the possible outcome like the one we did in lecture for two ordinary dice

The graph below shows a scatterplot of midterm scores plotted against homework scores The graph contains several points that correspond to unusually low homework scores and one of those scores is associated with the highest midterm score homework score as a predictor of midterm score Midterm 900 O 800 700 600 500 40 50 Removing this point will 60 70 HW decrease the correlation increase the correlation leave the correlation unchanged 80 The effect cannot be determined from the scatterplot 90 100 to have the average systolic blood pres

1 point If a hypothesis test is significant at level a 0 05 what is true of the P value P value 0 01 P value 0 05 P value 0 01 P value 0 05

1 A company wants to see if their medication reduces the amount of inflammation in the body They go about this by splitting their randomly sampled group in two Group A which is given the company s medication and Group B which is given a placebo a Classify this as an experimental or observational study Explain b Do you believe it is best for the company to collect quantitative or

1 point Assume that you are considering buying a car There is a probability of 0 4 that you will purchase a new vehicle and there is a probability of 0 5 that you will purchase a used vehicle There is no probability that you will buy more than one vehicle The probability that you will purchase no vehicle at all is 0 9 0 0000 0 1 1

A randomly sampled group of patients at a major U S regional hospital became part of a nutrition study on dietary habits Part of the study consisted of a 50 question survey asking about types of foods consumed Each question was scored on a scale from one most unhealthy behavior to five most healthy behavior The answers were summed and averaged The population of interest is the patients at the regional hospital A sample of n 15 patients produced the following statistics x 3 3 and s 1 2 A 99 confidence interval is given by 2 64 3 97 2 5 4 1 2 37 4 22 2 69 3 91 TOU

1 point A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension If the diet is effective the target is to have the average systolic blood pressure of this group be below 150 After six months on the diet an SRS of 28 patients had an average systolic blood pressure of x 143 with standard deviation s 16 The question is whether this if sufficient evidence that the diet is effective in meeting the target Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean u Based on the data the value of the one sample t statistic is 1 76 OO 2 32 1 51 1 94

2 A random sample of Starbucks employees from across the nation is asked how may cups of coffee they served on a given day The responses are as follows 24 36 55 17 62 41 42 37 28

1 point As part of a database of new births at a hospital some of the variables recorded are the age of the mother the marital status of the mother such as single married or divorced the weight of the baby and the sex of the baby Which of the following statements is or are true The sex of the baby and the marital status of the mother are categorical variables The individuals in this data set are births at the hospital All of the answer options are correct The age of the mother and the weight of the baby are quantitative variables

Sickle cell disease is a painful disorder of the red blood cells that in the United States affects mostly African Americans To investigate whether the drug hydroxyurea can reduce the pain associated with sickle cell disease a study by the National Institutes of Health gave the drug to 150 sickle cell sufferers and a placebo to another 150 Neither doctors nor patients were told who received the drug The number of episodes of pain reported by each subject was recorded This is an example of an observational study a double blind experiment an experiment but not a double blind experiment a paired data experiment

A 95 confidence is given by 15 20 The interval is based on a sample of size n 25 If we want to reduce the margin of error by half we need to double the sample size 0000 reduce the sample size to one quarter of the current sample size reduce the sample size by half quadruple the sample size