Statistics Questions

The figure below is similar to one that appeared in the report Digital Media Trends 15th Edition Courting the Consumer in a World of Choice The graph summarizes responses by generation to the question What is your favorite entertainment activity Generation Z may not be video first Respondents across generations ranked their favorite entertainment activity Percent 40 30 20 10 0 26 16 10 14 13 USE SALT 11 Play video Listen to games music 12 11 10 12 Browse the internet 11 Engage on social platforms 18 29 Watch TV shows or movies at home Suppose that the percentages given in the graph are baselt on independent representative samples of 900 people from each of the four generations Is there convincing evidence that the proportion of Boomers who say that their favorite entertainment activity is playing video games is less than this proportion for Generation X Test the relevant hypotheses using a 0 05 Let p be the population proportion of Boomers who say that their favorite entertainment activity is playing video games and p be the population proportion of Generation X who say that their favorite entertainment activity is playing video games Generation Z Millennials Generation X Boomers State the appropriate null and alternative hypotheses Enter for as needed

The Economist collects data each year on the price of a Big Mac in various countries around the world A sample of McDonald s restaurants in Europe in July 2021 resulted in the following Big Mac prices after conversion to U S dollars 6 33 4 74 2 54 4 71 3 76 3 41 2 86 LUSE SALT H The mean price of a Big Mac in the United States in July 2021 was 5 81 For purposes of this exercise you can assume it is reasonable to regard the sample as representative of European McDonald s restaurants Does the sample provide convincing evidence that the mean July 2021 price of a Big Mac in Europe is less than the reported U S price Test the relevant hypotheses using a 0 05 Hint See Example 12 11 State the appropriate null and alternative hypotheses in dollars Enter for as needed Ho Find the test statistic Round your answer to two decimal places MY NOTES Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context We reject Ho We do not have convincing evidence that the mean July 2021 price of a Big Mac in Europe is less than the reported U S price We fail to reject Ho We have convincing evidence that the mean July 2021 price of a Big Mac in Europe is less than the reported U S price We fail to reject Ho We do not have convincing evidence that the mean July 2021 price of a Big Mac in Europe is less than the reported U S price We reject H We have convincing evidence that the mean July 2021 price of a Big Mac in Europe is less than the reported U S price

Suppose that a random sample of size 64 is to be selected from a population with mean 50 and standard deviation 7 USE SALT a What are the mean and standard deviation of the sampling distribution of x Hx ox Describe the shape of the sampling distribution of x The shape of the sampling distribution of x is Select b What is the approximate probability that x will be within 0 5 of the population mean u Round your answer to four decimal places c What is the approximate probability that x will differ from by more than 0 8 Round your answer to four decimal places

Many people now turn to the Internet to get information on health related topics A research article used Flesch reading ease scores a measure of reading difficulty based on factors such as sentenc length and number of syllables in the words used to score pages on Wikipedia and on WebMD Higher Flesch scores correspond to more difficult reading levels The paper reported that for a representative sample of health related pages on Wikipedia the mean Flesch score was 26 6 and the standard deviation of the Flesch scores was 14 7 For a representative sample of pages from WebMD the mean score was 43 6 and the standard deviation was 19 6 Suppose that these means and standard deviations were based on samples of 40 pages from each site Is there convincing evidence that the mean reading level for health related pages differs for Wikipedia and WebMD Test the relevant hypotheses using a significance level of 0 05 Use for Wikipedia and for WebMD USE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context We reject Ho There is not convincing evidence that the mean reading level for health related pages differs for Wikipedia and WebMD We reject Ho There is convincing evidence that the mean reading level for health related pages differs for Wikipedia and WebMD We fail to reject Ho There is not convincing evidence that the mean reading level for health related pages differs for Wikipedia and WebMD Wo fall to reject Ho There is convincing evidence that the mean reading level for health related pages differs for Wikipedia and WebMD

In recent years concerns have been expressed about adverse health effects from amalgam dental restorations which include mercury The table below shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury based on the data from Neuropsychological and Renal Effects of Dental Amalgam in Children by Bellinger et al Journal of the American Medical Association Vol 295 No 15 Use a 0 05 significance level to test for independence between the type of restoration and sensory disorders Amalgam Dental Restorations Sensory Disorder No sensory disorder Amalgam Composite 36 231 28 239 O There is sufficient evidence to warrant rejection of the claim of independence between the type of restoration and adverse health conditions O There is not sufficient evidence to support the claim of independence between the type of restoration and adverse health conditions There is sufficient evidence to support the claim of independence between the type of

Find the median for the given sample data In ten trips to Las Vegas a person had the following net gains 2052 3538 4981 6887 3208 2052 6986 7492 6768 4511 Find the median net gain O 2052 00 O 5345 83

Use the given data to find the equation of the regression line Round the final values to three significant digits if necessary x 6 8 20 28 36 y 2 4 13 20 30 O y 2 79 0 950x Oy 2 79 0 897x O y 3 79 0 897x 0x 3 79 0801x

Given the linear correlation coefficient r and the sample size n determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation Use a significance level of 0 05 r 0 812 n 9 O Critical values r 0 666 significant linear correlation O Critical values r 0 666 no significant linear correlation O Critical values r 0 666 no significant linear correlation Critical valuesu OLL

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor Construct the 98 confidence interval for the true population proportion of all New York State union members who favor the Republican candidate O 0 301 p 0 445 0 308 p 0 438 O 0 304 p 0 442

Find the indicated probability 100 employees of a company are asked how they get to work and whether they work full time or part time the results are shown below If one of the 100 employees is randomly selected find the probability that the person drives alone or cycles to work 1 Public transportation 7 full time 8 part time 2 Bicycle 5 full time 4 part time 3 Drive alone 32 full 26 part time 4 Carpool 8 full time 10 part time O 0 43 O 0 67 O 0 58

Construct the indicated confidence interval for the difference between population proportions p P2 Assume that the samples are independent and that they have been randomly selected X 36 n 80 and x2 44 n 85 Construct a 95 confidence interval for the difference between population proportions P P2 O 0 249 P1 P2 0 631 O 0 269 P1 P2 0 631 O 0 298 P1 P2 0 602

Solve the problem A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8 4 hours and the standard deviation is 1 8 hours If 40 mechanics are randomly selected find the probability that their mean rebuild time exceeds 7 7 hours O 0 9634 O 0 9931

Solve the problem The weights of certain machine components are normally distributed with a mean of 8 81 g and a standard deviation of 0 06 g Find the two weights that separate the top 3 and the bottom 3 These weights could serve as limits used to identify which components should be rejected O 8 68 g and 8 97 g O 8 70 g and 8 92 g O 8 80 g and 8 82 g

Find the indicated percentile decile or quartile The weights in pounds of 30 newborn babies are listed below Find P16 5 5 5 7 5 8 5 9 6 1 6 1 6 4 6 4 6 5 6 6 6 7 6 7 6 7 6 9 7 0 7 0 7 0 7 1 7 2 7 2 7 4 7 5 7 7 7 7 7 8 8 0 8 1 8 1 8 3 8 7 O 5 9 O 6 1 O 6 0

Use the P value method to test the given hypothesis A nationwide study of American homeowners revealed that 64 have one or more lawn mowers A lawn equipment manufacturer located in Omaha feels the estimate is too low for households in Omaha Can the value 0 64 be rejected if a survey of 498 homes in Omaha yields 332 with one or more lawn mowers Use a 0 05 O There is sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is not 0 64 O There is sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is not 0 64 O There is not sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is not 0 64 O There is not sufficient evidence to warrant rejection of the claim that the proportion with

Compute the test statistic used to test the null hypothesis The National Transportation Association reports that more accidents are caused by cell phones than by drunken drivers The cell phone industry their own study to refute the claim They obtained 10 000 auto acciden reports and found that 15 were caused by drivers using cell phones If the actual rate for drunken driver accidents is 13 were the cell phone makers happy with the results H p 13 Use a 95 confidence level O 5 947 O 11 894

Use the traditional method to test the given hypothesis Assume that the population is normally distributed and that the sample has been randomly selected The standard deviation of math test scores at one high school is 16 1 A teacher claims that the standard deviation of the girls test scores is smaller than 16 1 A random sample of 22 girls results in scores with a standard deviation of 13 4 Use a significance level of 0 01 to test the teacher s claim O There is not sufficient evidence to warrant rejection of the claim that the standard deviation of the girl s tests scores is smaller than 16 1 O There is not sufficient evidence to support the claim that the standard deviation of the girl s tests scores is smaller than 16 1 O There is sufficient evidence to support the claim that the standard deviation of the girl s tests scores is smaller than 16 1 deviation of

Find the percentile for the data point Data set 16 24 56 32 16 40 72 72 88 24 24 72 48 8 72 data point 56 O 60 O 52 O 35

Find the indicated probability An airline estimates that 90 of people booked on their flights actually show up If the airline books 78 people on a flight for which the maximum number is 76 what is the probability that the number of people who show up will exceed the capacity of the plane O 0 0003 O 0 0026

Test the given claim by using the p value method of testing hypotheses Assume that the sample is a simple random sample selected from a normally distributed population Include the hypotheses the test statistic the p value and your conclusion Test the claim that for the adult population of one town the mean annual salary is given by 30 000 Sample data are summarized as n 17 the sample mean x bar 22 298 and s 14 200 Use a significance level of a 0 05 O There is sufficient evidence to support the claim that the mean annual salary is 30 000 O There is sufficient evidence to reject the claim that the mean annual salary is 30 000 There is not sufficient evidence to reject the claim that the mean annual salary is 30 000 OC There is not sufficient evidence to su pport the claim that

Find the necessary sample size The weekly earnings of students in one age group are normally distributed with a standard deviation of 60 dollars A researcher wishes to estimate the mean weekly earnings of students in this age group Find the sample size needed to assure with 9 percent confidence that the sample mean will not differ from the population mean b more than 2 dollars O 4887 O 82 4908

Use the empirical rule to solve the problem The amount of Jen s monthly phone bill is normally distributed with a mean of 75 and a standard deviation of 9 What percentage of her phone bills are between 48 and 102 O 99 99 O 68 26 O 99 74 O 95 44

Find the mean of the given probability distribution In a certain town 70 of adults have a college degree The accompanying table describes the probability distribution for the number of adults among 4 randomly selected adults who have a college degree Probability Among 4 Adults That They Have a College Degree P x 0 0081 0 0756 0 2646 0 4116 0 2401 O 2 00 O 2 70 0281 X ON 3 T 2 4

Use the given degree of confidence and sample data to construct a confidence interval for the population mean 39 packages are randomly selected from packages received by a parcel service The sample has a mean weight of 21 1 pounds and a standard deviation of 3 7 pounds What is the 95 percent confidence interval for the true mean weight of all packages received by the parcel service O 19 6 22 6 O 20 1 22 1 O 19 7 22 5

Use the data to create a stemplot The weights of 22 members of the varsity football team are listed below 144 152 142 151 160 152 131 164 141 153 140 144 175 156 147 133 172 159 135 159 148 171 O 13 135 14 1223699 15 0124478 16 04 17 125 13 135 14 0124478 15 1223699 16 04

Find the indicated probability The table below describes the smoking habits of a group of asthma sufferers Smoking Habits of Asthma Sufferers Occasional Smoker 37 34 71 Men Women Total Nonsmoker Doesn t Smoke 366 318 684 Regular Smoker 72 72 144 the answer is none of these choices O 0 591 O 0 462 Heavy Smoker 30 35 65 Total 505 459 964 If one of the 964 people is randomly selected find the probability that the person is a man or a heavy smoker

Find the indicated probability A bag contains 6 red marbles 3 blue marbles and 7 green marbles If a marble is randomly selected from the bag what is the probability that it is blue O 0 0625 O 0 231 O 0 188 O 0 333

Given the following data from a sample of 150 voters use the Chi Square Test to test for the dependence between political affiliation and the preferred candidate for mayor between Mayor McCheese and H R Pufnstuf Democrat Republican Other McCheese 19 46 15 Pufnstuf 31 19 20 5 Compute the Chi Square test statitistic 16 n

Green Blue 39 65 Jake wants to know if the spinner from his game is fair Given the results of 200 spins use the Chi Square Test X 7 88 to determine if the spinner has the same likelihood of landing on each of the four colors e pas gag 1 Compute the Chi Square test statistic Bygn SUR 52 7 00 red blue yellow green

Suppose 10 of students are veterans and 136 students are involved in sports How unusual would it be to have no more than 12 veterans involved in sports 12 veterans is about 8 8235 When working with samples of size 136 what is the mean of the sampling distribution for the proportion of veterans When working with samples of size 136 what is the standard error of the sampling distribution for the proportion of veterans Compute Pp 0 088235 P p 0 088235 NOTE Give results accurate to 5 decimal places Is this result unusual O Yes there is a less than 50 chance of this happening by random variation No there is at least a 50 chance of this happening by random variation

The Real Estate Group NY reports that the mean monthly rent for a one bedroom apartment without a doorman in Manhattan is 2514 Assume the standard deviation is 498 A real estate firm samples 110 apartments What is the probability that the sample mean rent is less than 2 580 95

The useful life of a bicycle bought at Basement mart fits a log normal distribution with a mean of 20 months and a standard deviation of 12 24 months Suppose that 64 bicycles are randomly chosen and let X the average useful life of a bicycle bought at Basement mart from a sample of 64 bicycles in months X

Engineers must consider the breadths of human heads when designing helmets The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6 1 in and a standard deviation of 0 9 in Using the Empirical Rule in what range would you expect to find the middle 95 of most head breadths Between and If you were to draw samples of size 46 from this population in what range would you expect to find the middle 95 of most averages for the breadths of human heads in the sample Between and

Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2 46 days note that times are measured continuously not just in number of days A random sample of 99 shipments are selected and their shipping times are observed Approximate the probability that the average shipping time is less than 2 13 days Enter your answer as a number accurate to 4 decimal places

The administrator at a local hospital states that on weekends the average wait time for emergency room visits is 10 minutes Based on discussions on the length of wait time to be seen in the ER over a weekend an employee disputes the administrator s claim The employee decides to test his hypothesis Over the course of a few weekends the employee records the wait time for 40 randomly selected patients The average wait time for these 40 patients is 11 minutes with a standard deviation of 3 minutes Does the employee have enough evidence to support his claim that the average ER wait time exceeds 10 minutes He tests at a 5 level of significance If the null hypothesis is rejected then the employee s conclusion is there is sufficient evidence to support the claim that the ER wait times exceed 10 minutes there is not sufficient evidence to support the claim that the ER wait times exceed 10 minutes Othere is sufficient evidence to warrant rejection of the original claim Othere is not sufficient evidence to warrant rejection of the original claim

According to a major credit card company the mean outstanding credit card debt of college undergraduates was 2 210 in 2007 with a standard deviation of 28 What test statistic is calcuated fo this scenario Oz score Ot value O null test O mean test Op value

According to a study the proportion of individuals in which cover their mouths when sneezing is 0 805 From a survey of 140 adults 132 cover their mouths when sneezing What test statistic is calcuated for thi scenario Z score null test O mean test p value t value

According to a survey of 1 190 adult college students the mean number of alcoholic beverages consumed per week is 10 with a standard deviation of 7 beverages What test statistic is calcuated for this scenario Op value O mean test O null test Ot value Oz score

If a claim is in the null hypothesis and we reject the null hypothesis then the conclusion would be there is not sufficient sample evidence to support the original claim there is sufficient evidence to warrant rejection of the original claim the sample data support the original claim Othere is not sufficient evidence to warrant rejection of the original claim

There is a functional relationship between the price of a small tablet p and weekly demand s Price p Weekly Demand s 1 000s 209 203 196 188 183 174 150 170 190 210 230 250 a Find the linear model that best fits this data using regression and enter the model below Round the slope to the nearest hundredth and the constant to the nearest whole s T p

Item D ading in the visual display of data below Misleading pie chart Item A Item B Item C 42 5 Regular pie chart 11 42 item A item 8 item C Item D Item C appears to be at least as large as Item A in the misleading pie chart whereas in actuality it is less than half as large Colors on the chart are too dark and distort the data The percentages do not add up to 100 The chart is too small

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution How many students had less than 60 social interactions for the week 34 62 21 13 Number of Social Interactions 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 Frequency 8 13 13 15 10 12 5 3 1 3

A recent survey revealed that 92 of computer owners in a certain city have access to the Internet Describe the population this statement is referring to all computer owners in the country all computer owners in the city all residents of the city all internet users of the city

For the set of points above determine whether an exponential function a linear function or a quadratic function is the best choice for modeling the data quadratic function exponential function linear function

A fair coin is tossed two times in succession The set of equally likely outcomes is HH HT TH TT Find the probability of getting the same outcome on each toss 1123 03 0 4 1 14

of traffic accid nts at intersections with raised medians with rates at intersections with two way left turn lanes They found that out of 4656 accidents at intersections with raised medians 2112 were rear end accidents and out of 4574 accidents at two way left turn lanes 2024 were rear end accidents Part 1 of 2 a Assuming these to be random samples of accidents from the two types of intersection construct a 99 9 confidence for the difference between the proportions of accidents that are of the rear end type at the two types of intersection Use the TI 84 calculator and round the answers to three decimal places Let p represent the population for accidents at intersections with raised medians A 99 9 confidence interval for the difference between the proportions of accidents that are of the rear end type at the two types of intersection is I P P Part 1 2 Part 2 of 2 b Does the confidence interval contradict the claim that the proportion of rear end accidents is the same at both types of intersection Because the confidence interval Choose one 0 it Choose one that the pr the claim

A recent study examined the effects of carbon monoxide exposure on a group of construction workers The following table presents the numbers of workers who reported various symptoms along with the shift morning evening or night that they worked Influenza Headache Weakness Shortness of Breath Send data to Excel Part 0 4 Morning Shift 17 32 11 4 Part 1 of 4 Evening Shift 10 27 18 7 Test the hypothesis of independence Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator What do you conclude Night Shift 18 6 9 10 State the null and alternate hypotheses Ho The shift and reported symptoms Choose one H The shift and reported symptoms Choose one independent independent

Prior to a new drive through system the mean wait time at a certain fast food restaurant was 96 seconds Use the data in the table below to decide whether the evidence suggests the mean wait time is different than 96 seconds with their new system Assume wait times are normally distributed and use an a 0 10 significance level Use the p value approach 104 8 101 5 84 6 91 1 81 8 81 a For this study we should use t test for a population mean b The null and alternative hypotheses would be Ho u 96 96 0 848 91 9 H P c The test statistic V d The p value 0 4182 e The p value is a f Based on this we should Select an answer the null hypothesis g Thus the final conclusion is that 89 6 101 9 please show your answer to 3 decimal places Please show your answer to 4 decimal places 106 2 O The data suggest the population mean is not significantly different at a 0 10 so there is not sufficient evidence to conclude that the mean wait time is different The data suggest the population mean is not different at a 0 10 so there is sufficient evidence to conclude that the mean wait time is different O The data suggest the populaton mean is significantly different at a 0 10 so there is sufficient evidence to conclude that the mean wait time is different Explain how you found the p value in the last problem

What is the relationship between the attendance at a major league ball game and the total number of runs scored Attendance figures in thousands and the runs scored for 9 randomly selected games are shown below Attendance Runs 60 16 18 52 57 19 14 3 9 16 9 O H 0 The p value is 0 0289 9 a Find the correlation coefficient r 0 72 b The null and alternative hypotheses for correlation are Hor 0 30 43 53 11 12 10 Round to 2 decimal places Round to four decimal places c Use a level of significance of a 0 05 to state the conclusion of the hypothesis test in the context of the study There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored Thus the use of the regression line is not appropriate There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance d The equation of the linear regression line is X There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored Thus the regression line is useful Please show your answers to two decimal places e Use the model to predict the runs scored at a game that has an attendance of 5 thousand people Runs scored Please round to two decimal places f Interpret the slope of the regression line in the context of the question As x goes up y goes up The slope has no practical meaning since the total number runs scored in a game must be positive For every additional thousand people who attend a game there tends to be an average increase of 0 15 runs scored

Match the terms to the correct symbols n gives the Population Mean Sample Mean Population Size Sample Size Population Standard Deviation Sample Standard Deviation gives the Population Mean Sample Mean Population Size Sample Size Population Standard Deviation Sample Standard Deviation gives the Population Mean Sample Mean Population Size Sample Size Population Standard Deviation Sample Standard Deviation