Statistics Questions and Answers

The box plot shows the heights of grade 7 students in two random samples from two different schools The sample item from each school is 30 of the student population School A School B B Heights of Grade 7 Students 4 Based on the box plot which comparison is true Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools D 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Height inches Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in t medians of grade 7 student heights at the schools Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in th interquartile ranges of grade 7 student heights at the schools Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in medians of grade 7 student heights at the schools

27 Which choice shows a set of data that could be represented by the box plot shown below 0 5 10 A 1 3 5 6 6 8 13 14 19 20 B 1 2 3 5 7 8 8 13 19 20 1 5 5 6 6 6 8 13 19 20 13567 7 8 13 10 20 15 20

The dot plot shows the Each dot represents 1 country 7 8 B 18 1 14 19 23 9 What is the mean number of public holidays A 20 17 10 15 11 12 13 Number of Public Holidays 17 18 16 14

7 The dot plot shows the number of public Each dot represents 1 country 7 8 B 18 1 c 14 19 9 What is the mean number of public holidays A 20 17 D 23 10 11 12 13 14 Number of Public Holidays 15 16 DO 17 18

Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination She would like to choose a destination with a high median temperature and a small interquartile range She constructed box plots shown in the diagram below Ocean Beach Serene Shores Whispering Palms 70 75 80 85 90 95 100 70 75 80 85 90 95 100 Which destination has a median temperature above 80 degrees and the smallest interquartile range A Pelican Beach B Ocean Beach D Whispering Palms Pelican Beach Serene Shores

line plots below to compare the quiz scores for her first period math class and her second period math class She gave the same quiz to each class B QUIZ SCORES First Period Class X X X X X X AHH 0 1 2 3 4 5 6 7 8 9 10 Points X X Second Period Class X X X X X X X X X X X X X X 0 1 2 3 X X 4 5 6 Points 7 8 9 10 What conclusion can Ms Andrews make about the performance of her first and second period classes A The second period class scores had a higher mean than the first period class scores The first period class had a higher median score than the second period class

B The students in a study group each measured the thickness of their math notebooks The results are shown in the lineplot below A 1 inches 8 1 B 2 inches 2 2 8 7 C 2 inches 8 3 8 Thickness of Notebook inches 3 D 2 inches 8 4 8 If the students stack their notebooks one on top the other what will be the total thickness of the stack 5 8 68

20 The principal of the school is looking over grade reports specifically scores on math quizzes This box and whisker plot shows the results Find median and range in the given box plot Math quiz scores 50 Median 60 70 80 and Range 90

5 The test scores of the students in Mr Duffy s class are shown on the line plot below MR DUFFY S CLASS x XX XXX X X X X x X X X X X A 60 65 70 75 80 85 90 95 100 Most of the students in Ms Guzman s class scored higher than most of the students in Mr Duffy s class on the same test Which line plot could represent the test scores of the students in Ms Guzman s class MS GUZMAN S CLASS A x x B X X X X 4 1 X X X 60 65 70 75 80 85 90 95 100 MS GUZMAN S CLASS X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 60 65 70 75 80 85 90 95 100

BOX PLOT The box and whisker plot describes the number of absences for Mr Fitz s students F 4 6 8 10 12 14 According to the plot what percent of the students were absent between 4 and 6 days A 100 B 50 25 D 75

Use the box plot below to fill in the blanks to the five number summary below Cost of each lunch for the month in dollars H 4 5 Minimum Maximum Median First Quartile Third Quartile 6 7 8 H 9 10

3 12 points Graph the function y 22 Find z and y intercepts hor izontal and vertical asymptotes all critical numbers intervals of in de creasing local absolute max min x 1 Draw your graph on the next page

Below is a hypothesis test set up by a student who recently took introductory statistics Ho x 5 HA X 5 The sample mean of 100 cases used to implement the hypothesis test is x 4 2 Which of the following statements are accurate i This is a one sided hypothesis test ii There is an error in how these hypotheses were constructed iii It would be reasonable to swap for z in the alternative hypothesis Oi only O ii only iii only Oi and ii Oi and iii O ii and iii

Less than 55 of Internet users pay bills online Express the null and alternative hypotheses in symbolia form for this claim enter as a percentage Ho P H P Use the following codes to enter the following symbols

A New York Times article titled For Runners Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury One position supported running on soft surfaces to relieve joints that were in recovery from injury The second position supported running on hard surfaces since soft surfaces can be uneven which may make worse those injuries a soft surface was intended to help Suppose we are given sufficient funds to run an experiment to study this topic With no studies to support either position which of the following hypotheses would be appropriate O The first position is more sensible so this should be a one sided test In this case we should form the alternative hypothesis around the second position O The second position makes the more sense so this should be a one sided test In this case we should form the alternative hypothesis around the first position O Because we would be interested in any difference between running on hard and soft surfaces we should use a two sided hypothesis test O Because there is uncertainty we should postpone defining the hypotheses until after we collect data to guide the test

A commonly cited standard for one way length duration of school bus rides for elementary school children is 30 minutes A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one way commute time of 38 minutes with a standard deviation of 8 minutes Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes O Ho H 30 HA x 38 O Ho x 38 HA H 30 O Ho H 30 HA 30 OHA H 30 Ho x 30 Ho H 30 HA 30

To evaluate the effectiveness review sessions a professor gave a pre test before the review and a post test after The results are shown in the table below 50 REE 19 Pre test 1 Post test 22 7 0 49 60 79 37 67 57 60 61 65 92 16 35 13 Difference d x 1 22 57 22 33 25 63 4 24 47 10 X0 23 37 78 17 43 22 0 38 20 1 The null and alternative hypotheses would be Ho Pa H Ha o o OF o o 58 Can we say that the review session significantly harms test performance at 10 significance level 8 8 5 8 o

post test after The results are shown in the table below Pre test 1 Post test 48 58 46 55 65 55 60 60 46 59 42 63 42 69 Difference d 22 21 68 11 60 16 62 3 17 76 21 13 9 8 14 Can we say that the review session makes a significant difference on test performance at 5 significance level 1 The null and alternative hypotheses would be Ho Ha Select an answer H Ha Select an answer 2 The tail type of the test is Select an answer 3 The sample statistic d is

Solve the equation for the variable Write your solution as a simplified root If there are 2 solutions list them with a comma separating them Example 27 27 or 3 5 3 5 If there is no solution enter DNE 4x 8 392 X

Solve the radical equation 19x 2 3x Enter the smallest value for a first X1 X2

Solve 2x 7 3

olve the absolute value equation or indicate that the equation has no solution with x 2 7

1 4 x 4 3x 6 3

You spin the spinner once 3 2 What is P divisor of 42 Simplify your answer and write it as a fraction or whole number

3 If the population deviation o is known and we wish to estimate the population mean u with 95 confidence what is the appropriate critical value z to use a 1 28 b 1 645 c 1 96 d 2 33 The lower limit of a confidence interval at the 95 level of confidence for the population proportion when the sample size of 100 had 30 successes is a 0 3898 b 0 2102 d 0 3041 4 0 2959 1

Complete parts a through d for the sampling distribution of the sample mean shown in the accompanying graph Click the icon to view the graph a What is the value of The value of is 300 b What is the value of o The value of o is 40 c If the sample size is n 16 what is likely true about the shape of the population OA The shape of the population is skewed left B The shape of the population is approximately normal OC The shape of the population is skewed right OD The shape of the population cannot be determined d If the sample size is n 16 what is the standard deviation of the population from which the sample was drawn The standard deviation of the population from which the sample was drawn is

post test after The results are shown in the table below Pre test 1 59 57 66 44 73 64 59 72 51 Post test 2 65 31 56 48 18 36 8 67 36 63 4 Difference d x2 1 28 0 o 0 2 The tail type of the test is Left Tailed 3 The sample statistic d is 1 44 7 28 7 1 The null and alternative hypotheses would be Ho Pa H Pd 6 q o B q OF Can we say that the review session significantly harms test performance at 5 significance level E OF E B B

Several years ago 47 of parents who had children in grades K 12 were satisfied with the quality of education the students receive A recent poll asked 1 105 parents who have children in grades K 12 if they were satisfied with the quality of education the students receive Of the 1 105 surveyed 468 indicated that they were satisfied Construct a 95 confidence interval to assess whether this represents evidence that parents attitudes toward the quality of education have changed What are the null and alternative hypotheses Ho P versus H p Type integers or decimals rounded to two decimal places as needed Use technology to find the 95 confidence interval We are 95 confident the proportion of parents who had children in grades K 12 that were satisfied with the quality of education the students receive is between and Type integers or decimals rounded to two decimal places as needed What is the correct conclusion O A Since the interval does not contain the proportion stated in the null hypothesis there is insufficient evidence that parents attitudes toward the quality of education have changed OB Since the interval contains the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed OC Since the interval contains the proportion stated in the null hypothesis there is insufficient evidence that parents attitudes toward the quality of education have changed O D Since the interval does not contain the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed

As part of a survey 17 college graduates and 18 non graduates were asked How many hours did you spend at your job last week The results are shown in the stem and leaf display below Answer the questions that follow Number of hours at work Graduates Non graduates 996 223678 87730 312468 9974310 40003778 32 53 Key 26 6 2 2 22 a What were the ranges for the two groups 0 0 Graduates Non graduates b Which group had the higher median number of hours O Graduates O Non graduates O The medians were the same c Which group had more responses in the 50s O Graduates O Non graduates Fach X 5

A certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux The manufacturer of the drug claims that more than 91 of patients taking the drug are healed within 8 weeks In clinical trials 206 of 223 patients suffering from acid reflux disease were healed after 8 weeks Test the manufacturer s claim at the x 0 05 level of significance Because npo 1 Po Round to one decimal place as needed What are the null and alternative hypotheses 10 the sample size is Ho versus H Type integers or decimals Do not round Find the test statistic Zo Zo Round to two decimal places as needed Find the P value P value Choose the correct conclusion below 5 of the population size and the sample the requirements for testing the hypothesis satisfied Round to three decimal places as needed O A Reject the null hypothesis There is insufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks OB Reject the null hypothesis There is sufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks OC Do not reject the null hypothesis There is insufficient evidence to conclude that more than 91 of patients taking the drug are healed within 8 weeks O D Do not reject the null hypothesis There is sufficient evidence to conclude more than 91 of patients taking the drug are healed within 8 weeks

19 Which of the following is a negative side effect of using macroeconomic policies to offset a recessionary gap A crowding out of private investment B possibly unpredictable consequences of the stabilizing macroeconomic policies a higher aggregate price level C D all of the answer choices provided are negative side effect of using macroeconomic policies

Two professors at a local college developed a new teaching curriculum designed to increase students grades in math classes In a typical developmental math course 56 of the students complete the course with a letter grade of A B or C In the experimental course of the 14 students enrolled 11 completed the course with a letter grade of A B or C Is the experimental course effective at the x 0 025 level of significance Complete parts a through g a State the appropriate null and alternative hypotheses Ho V versus H Type integers or decimals Do not round b Verify that the normal model may not be used to estimate the P value Because npo 1 Po Round to one decimal place as needed c Explain why this is a binomial experiment 10 the normal model be used to approximate the P value There is a number of trials with independent and the probability of success is fixed at Type an integer or a decimal Do not round d Determine the P value using the binomial probability distribution State your conclusion to the hypothesis test First determine the P value P value Round to three decimal places as needed Is there sufficient evidence to support the research that the experimental course is effective for each trial The trials O A No do not reject the null hypothesis because the P value is greater than a There is insufficient evidence to conclude that the experimental course is effective OB Yes reject the null hypothesis because the P value is less than a There is sufficient evidence to conclude that the experimental course is effective OC No reject the null hypothesis because the P value is less than a There is insufficient evidence to conclude that the experimental course is effective 10 the sample size is O D Yes do not reject the null hypothesis because the P value is greater than a There is sufficient evidence to conclude that the experimental course is effective e Suppose the course is taught with 42 students and 33 complete the course with a letter grade of A B or C Verify whether the normal model may now be used to estimate the P value Because npo 1 Po the normal model 5 of the population size and the sample be used to approximate the P value Round to one decimal place as needed f Use the normal model to obtain and interpret the P value State your conclusion to the hypothesis test First find the test statistic Zo Zo Round to two decimal places as needed Now determine the P value

Twenty years ago 56 of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science A recent survey found that 288 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science Do parents feel differently today than they did twenty years ago Use the 0 01 level of significance Because npo 1 Po L Round to one decimal place as needed What are the null and alternative hypotheses 10 the sample size is 5 of the population size and the sample the requirements for testing the hypothesis satisfied Ho versus H Type integers or decimals Do not round Find the test statistic Zo Round to two decimal places as needed Find the P value P value Round to three decimal places as needed Determine the conclusion for this hypothesis test Choose the correct answer below O A Since P value a reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today OB Since P value a do not reject the null hypothesis and conclude that there is not sufficient evidence that parents feel differently today OC Since P value a do not reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today O D Since P value a reject the null hypothesis and conclude that there is not sufficient evidence that parents feel differently today

Test the hypothesis using the P value approach Be sure to verify the requirements of the test Ho p 0 84 versus H p 0 84 n 500 x 410 0 05 Is npo 1 Po 10 Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal Do not round O A No because npo 1 Po OB Yes because npo 1 Po Now find p 6 Type an integer or a decimal Do not round Find the test statistic zo Zo Round to two decimal places as needed Find the P value P value Round to three decimal places as needed State the conclusion of the hypothesis test the P value is than g

Explain what a P value is What is the criterion for rejecting the null hypothesis using the P value approach Explain what a P value is Choose the correct answer below OA A P value is the value used to designate the area a in either the left or right tail of the normal curve OB A P value is the number of standard deviations that the observed proportion is from the proportion stated in the null hypothesis OC A P value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true What is the criterion for rejecting the null hypothesis using the P value approach Choose the correct answer below OA If P value a reject the null hypothesis OB If P value Za for a left tailed test or if P value Za for a right tailed test or if P value Za 2 or P value Za 2 for a two tailed test then reject the null hypothesis OC If P value a reject the null hypothesis

Managers of a sports arena s parking garage keep track of the duration of time customers park their cars in the garage Shown in the stem and leaf display below is a sample of such parking durations in minutes For this sample 17 of the durations were from weekday use of the garage and 20 were from weekend use Answer the questions that follow Parking durations minutes Weekday Weekend 952 155 650 16 11356 9761 17 114 46699 9851 18 246 852 19 177 Key 152 2 15 5 155 a What were the ranges of parking durations for the two groups Weekday Weekend b Which group had the higher median parking duration O Weekday O Weekend O The medians were the same c Which group had more parking durations in the 150s X

Side effects of Avandia Rosiglitazone is the active ingredient in the controversial type 2 diabetes medicine Avandia and has been linked to an increased risk of serious cardiovascular problems such as stroke heart failure and death A common alternative treatment is Pioglitazone the active ingredient in a diabetes medicine called Actos In a nationwide retrospective observational study of 227 571 Medicare beneficiaries aged 65 years or older it was found that 2 593 of the 67 593 patients using Rosiglitazone and 5 386 of the 159 978 using Pioglitazone had serious cardiovascular problems These data are summarized in the contingency table below treatment Yes Pioglitazone 5 386 Rosiglitazone 2 593 7 979 Total No 154 592 65 000 219 592 a What proportion of all patients had cardiovascular problems Total 159 978 67 593 227 571 b If the type of treatment and having cardiovascular problems were independent about how many patients in the Rosiglitazone group would we expect to have had cardiovascular problems

0 Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture However their nondegradable nature has prompted development of environmentally friendly composites using natural mate rials The article Properties of Waste Silk Short Fiber Cellulose Green Composite Films J of Composite Materials 2012 123 127 reported that for a sample of 10 specimens with 2 fiber content the sample mean tensile strength MPa was 51 3 and the sample standard deviation was 1 2 Suppose the true average strength for 0 fibers pure cellulose is known to be 48 MPa Does the data provide compelling evi dence for concluding that true average strength for the WSF cellulose composite exceeds this value

The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan Each patient entering the program was designated an official heart transplant candidate meaning that they were gravely ill and would most likely benefit from a new heart Some patients got a transplant and some did not The variable transplant indicates which group the patients were in patients in the treatment group got a transplant and those in the control group did not Of the 34 patients in the control group 30 died Of the 69 people in the treatment group 45 died Another variable called survived was used to indicate whether the patient was alive at the end of the study Turnbull Brown and Hu 1974 a What is the difference between the proportion of patients who died in the treatment and control groups treatment control 0 231 o b One approach for investigating whether the treatment is effective is to use a randomization technique Fill in the blanks with a number or phrase whichever is appropriate We write alive on 28 cards representing all the patients in the sample who were alive at the end of the study and deceased on 75 ocards representing patients who were not Then we shuffle these cards and split them into two groups one group of size 69 of representing treatment and another group of size 34 o representing control We calculate the difference between the proportion of cards in the treatment and control groups treatment control and record this value We repeat this 100 times to build a distribution centered at 0 o Lastly we calculate the fraction of simulations where the simulated differences in proportions are lower than the difference of observed in our sample If this fraction is low we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative

An article in the San Jose Mercury News stated that students in the California state university system take 4 5 years on average to finish their undergraduate degrees Suppose you believe that the mean time is longer You conduct a survey of 49 students and obtain a sample mean of 5 1 years with a sample deviation of 1 2 years Conduct a hypothesis test at a 0 01 Ho H X is the Find the p value show your work here Indicate the correct decision Alpha and p Decision Reason for this decision

A variable is normally distributed with mean 23 and standard deviation 8 Round your answers to the nearest hundredth as needed a Determine the z score for x 28 2 b Determine the z score for x 18 z c What value of x has a z score of 0 88 x d What value of x has a z score of 0 4 x e What value of x has a z score of 0 x

2 A coach wishes to show the relationship between the of fouls committed and the total points scored by their opponent during the season Which of the following graphs would likely be most useful if the coach has a sample of 24 games of data c Box Whisker plot d Scatterplot a Bar chart b Pie chart

12 A recent sample of 40 stores in North Dakota indicated an average x number of days they held Christmas Sales of 15 with a standard deviation s of 3 days Use a Student t distribution to construct a 95 confidence interval 90 CI to

GPAS at CCSU are normally distributed with a mean of 2 49 and a standard deviation of 0 49 Find the z score for a GPA of 3 46 O 0 3878 O 0 9388 O 1 469 O 1 204 O 1 531

The lower limit of a confidence interval at the 95 level of confidence for the population proportion when the sample size of 100 had 30 successes is a 0 3898 b 0 2102 c 0 2959 d 0 3041 5 A 99 confidence interval estimate for a population mean u is determined to be 85 58 to 96 62 If the confidence level is reduced to 90 the confidence interval for 4 a becomes wider c becomes narrower 6 b remains the same d None of these From a sample of 200 items 12 items are defective The point estimate of the population proportion p defective will be a 12 b 0 06 c 16 67 d 0 12 7 In order to estimate the average number of miles that students who live off campus commute to classes every day the following statistics were given n 50 x 5 21 and s 2 48 The point estimate of the true population mean is a 1 96 b 2 10 c 5 21 d 7 07

CHAPTER 8 I 1 One way to reduce the margin of error in a confidence interval is to decrease the confidence coefficient a I II Multiple Choice If a 90 confidence interval estimate for the difference between two population proportions is to be constructed then the confidence coefficient a would be a 0 10 b 0 90 c 0 05 d 0 45 3 If the population deviation o is known and we wish to estimate the population mean with 95 confidence what is the appropriate critical value z to use True or False 2

95 CI 9 A random sample of 60 people revealed that 37 of them believed the new mayor was managing her job very well Use the Plus Four method to construct a 90 confidence interval for p the population proportion of people who believe the mayor is managing her job very well p 90 CI to 10 Sketch the confidence terval for 8 on a normal curve to

III STATISTICAL CONCEPTS APPLIED QUESTIONS Show your calculations Write complete sentences 8 A random sample of 45 door to door encyclopedia salespersons were asked how long on average they were able to talk to the potential customer Their answers revealed a mean of 8 5 minutes with a standard deviation of 3 minutes Give a point estimate for the average conversation length and calculate a 95 confidence interval OLGL to

3 BONUS These can help your score they cannot hurt your score Chapters 1 2 1 A sample of students who has taken a calculus test has a mean 60 2 a mode 72 and a median 72 Based on this information the distribution of scores is a symmetric b right skewed c left skewed d bimodal

5 0 10 points A small pond contains seven catfish and two bluegill If seven fish are caught at random with replacement what is the probability that all of them are catfish 17 83 47 28 Feedback Based on answering incorrectly The probability of success is 7 9 Then use the your calculator to calculate the binomial probability ng about the scenar probability of rolling a 4 exactly Here n is the number of trials which a is the number of successes w p is the probability of success or sided die So n is already given as 20 If you were referring to a different se provide them so that I can assist you B9O 2 2