Statistics Questions

DATAfile IntHotels You may need to use the appropriate technology to answer this question Hotel room pricing changes over time but is there a difference between Europe hotel prices and U S hotel prices The file IntHotels contains changes in the hotel prices for 47 major European cities and 53 major U S cities t a On the basis of the sample results can we conclude that the mean change in hotel rates in Europe and the United States are different Develop appropriate null and alternative hypotheses Let the population mean change in hotel rates in Europe and let the population mean change in hotel rates in the United States Enter for as needed Ho H b Use a 0 01 Calculate the test statistic Round your answer to three decimal places Calculate the p value Round your answer to four decimal places p value What is your conclusion O Reject Ho The mean change in hotel rates in Europe and the United States are not different O Reject Ho The mean change in hotel rates in Europe and the United States are different Do not reject Ho The mean change in hotel rates in Europe and the United States are different O Do not reject Ho The mean change in hotel rates in Europe and the United States are not different

The following information was obtained from matched samples taken from two populations Assume the population of differences is normally distributed Individual 1 2 3 4 5 Method 1 Method 2 7 5 6 7 5 7 7 4 8 9 The point estimate of the difference between the means of the two populations Method 1 Method 2 is 1 and the standard deviation is 2 24 The null hypothesis tested is Ho H 0 Find the tes statistic for the difference between the two population means 0 2 O 1 0 0 02

The following information was obtained from matched samples taken from two populations The daily production rates for a sample of workers before and after a training program are shown below Assume the population of differences is normally distributed Worker Before 00 O 1 00 1 77 1 2 3 4 5 6 7 21 26 28 24 23 21 18 After 23 24 28 21 26 20 19 The point estimate for the difference between the two population means is 0 The null hypothesis to be tested is Ho 0 Find the test statistic O 1 96

You may need to use the appropriate appendix table or technology to answer this question The following information was obtained from matched samples taken from two populations The daily production rates for a sample of workers before and after a training program are shown be Assume the population of differences is normally distributed Worker 1 2 3 4 5 6 7 Before After 21 26 28 24 23 21 18 24 25 29 22 27 21 20 Given that the null hypothesis to be tested is Ho H 0 at a 0 05 and the test statistic is 1 04 O the alternative hypothesis should be revised the null hypothesis should be revised O the null hypothesis should not be rejected the null hypothesis should be rejected

You may need to use the appropriate appendix table or technology to answer this question A random sample of 97 tourists in Chattanooga showed that they spent an average of 2 830 in a week with a standard deviation of 123 A sample of 73 tourists in Orlando showed that they s an average of 2 890 in a week with a standard deviation of 135 We are interested in determining if there is any significant difference between the average expenditures of all the tourists who visited the two cities a Determine the degrees of freedom for this test Round your answer down to the nearest integer X 0 b Compute the test statistic Use Chattanooga Orlando Round your answer to three decimal places c Compute the p value Round your answer to five decimal places d What is your conclusion Let a 0 02 O Reject Ho We can conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando O Do not reject Ho We cannot conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando O Reject Ho We cannot conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Qriando O Do not reject Ho We can conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando

3 Use the probability distribution or histogram to find the a mean b variance c standard deviation and d expected value of the probability distribution and e interpret the results The histogram shows the distribution of household sizes in country A for a recent year a The mean is Type an integer or a decimal Do not round b The variance is Round to two decimal places as needed c The standard deviation is Round to two decimal places as needed d The expected value is Type an integer or a decimal Do not round e Interpret your results Select all that apply A The average household is expected to have either 2 or 3 people B The average household is expected to have either 1 or 2 people C Most of the household sizes differ from the expected value by 2 or people AP x 0 40 0 30 0 253 0 20 0 10 0 00 0 328 0 149 0 158 2 3 Household Size 0 063 0 049

A comparative study of organic and conventionally grown produce was checked for the presence of E coli Results are summarized below Sample Size E coli Prevalence O Organic Conventional C Ho P P 0 H P P 0 O Ho P1 P 0 Ha P P 0 Is there a significant difference in the proportion of E coli in organic vs conventionally grown produce Test at a 0 10 Let d Organic Conventional a Formulate the hypotheses Ho P P 0 Ha P P 0 Ho P1 P 0 Ha P1 P 0 Ho P1 Ha P1 200 P 0 P 0 520 2 21 b What is the value of the test statistic Round your answer to three decimal places 4 100 x c What is the p value Round your answer to three decimal places p value d What is your conclusion O Do not reject Ho We cannot conclude that there is a significant difference in the proportion of E coli in organic vs conventional produce O Do not reject Ho We can conclude that there is a significant difference in the proportion of E coli in organic vs conventional produce O Reject Ho We can conclude that there is a significant difference in the proportion of E coli in organic vs conventional produce O Reject Ho We cannot conclude that there is a significant difference in the proportion of E coli in organic vs conventional produce 9

You may need to use the appropriate appendix table or technology to answer this question During recent primary elections the democratic presidential candidate showed the following pre election voter support in Alabama and Mississippi State Alabama Mississippi Voters Surveyed Ho P P 0 Ha P P 0 827 O Ho P P 0 H P P 0 Ho P P 20 Ha P P 0 630 Voters Favoring the Democratic Candidate 463 We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states Use Alabama Mississippi a Provide the hypotheses O Ho P P 0 Ha P P 20 384 Ho P1 P 0 Ha P P 0 b Compute the test statistic Round your answer to three decimal places c Determine the p value and at a 0 05 level of significance test the above hypotheses We do not reject Ho There is no significant difference We do not reject Ho There is a significant difference We reject Ho There is no significant difference

You may need to use the appropriate appendix table or technology to answer this question A poll was taken this year asking college students if they considered themselves overweight A similar poll was taken five years ago Results are summarized below Present Sample Previous Sample Sample Size b What is your conclusion 296 279 Number Considered Themselves Overweight 153 133 Has the proportion increased significantly Let a 0 05 Use Present Previous a What is the p value Round your answer to four decimal places p value O We do not reject Ho There is no significant difference O We do not reject Ho There is a significant difference O We reject Ho There is no significant difference O We reject Ho There is a significant difference

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year The results are shown below Under Age of 18 Over Age of 18 7 1 300 7 1 500 Number of accidents 160 Number of accidents 120 We are interested in determining if the accident proportions differ between the two age groups Find the pooled estimator of the population proportion 0 010 0 100 0 203 0 215

probability distribution below The number of overtime hours worked in one week per employee Overtime hours Probability a Find the mean variance and standard deviation of the probability distribution Find the mean of the probability distribution Find the variance of the probability distribution Round to one decimal place as needed Round to one decimal place as needed Find the standard deviation of the probability distribution Round to one decimal place as needed b Interpret the results in the context of the real life situation 0 0 021 1 0 058 OA An employee works an average 3 5 of overtime hours per week with a standard deviation of approximately 4 hours OB An employee works an average of 1 9 overtime hours per week with a standard deviation of approximately 1 4 hours C An employee works an average of 1 4 overtime hours per week with a standard deviation of approximately 3 5 hours D An employee works an average of 3 5 overtime hours per week with a standard deviation of approximately 1 4 hours 2 0 136 3 0 309

You may need to use the appropriate appendix table or technology to answer this question A comparative study of organic and conventionally grown produce was checked for the presence of E coli Results are summarized below Sample Size E coli Prevalence Organic Conventional Ho P Ha P1 Ho P1 H P Is there a significant difference in the proportion of E coli in organic vs conventionally grown produce Test at a 0 10 Let d Organic Conventional A a Formulate the hypotheses P 0 P 0 P 0 P 0 Ho P1 P 0 Ha P P 0 Ho P Ha P Ho P1 P 0 Ha P P 0 200 P 0 P 0 520 2 21 b What is the value of the test statistic Round your answer to three decimal places

You may need to use the appropriate appendix table or technology to answer this question The office of records at a university has stated that the proportion of incoming female students who major in business has increased A sample of female students taken several years ago with a sample of female students this year Results are summarized below Previous Sample Present Sample Sample Size 257 331 No of Females Majoring in Business 51 X 72 Has the proportion increased significantly Test at a 0 10 Use Present Previous O We do not reject Ho There is no significant difference O We do not reject Ho There is a significant difference O We reject Ho There is no significant difference We reject Ho There is a significant difference

46 5 Keep working At least one of the answers above is NOT correct Getting things wrong is part of learning 1 point Is the number of games won by a major league baseball team in a season related to the team batting average The table below shows the number of games won and the batting average in thousandths of 8 teams Team Games Won Batting Average 1 2 3 4 5 678 80 85 90 118 93 107 72 87 265 288 287 262 286 273 268 285 Using games won as the explanatory variable x do the following a The correlation coefficient is r b The equation of the least squares line is y 0 051 0 00169x 259 25 i e trendline equation with 5 digits of accuracy for both coefficients hotting averages which is explained by x games won is Keep Working 46 5

Determine whether the random variable is discrete or continuous a The exact time it takes to evaluate 27 72 b The number of fish caught during a fishing tournament c The weight of a T bone steak d The number of light bulbs that burn out in the next week in a room with 13 bulbs e The number of people with blood type A in a random sample of 15 people a Is the exact time it takes to evaluate 27 72 discrete or continuous OA The random variable is continuous OB The random variable is discrete b Is the number of fish caught during a fishing tournament discrete or continuous OA The random variable is continuous OB The random variable is discrete c Is the weight of a T bone steak discrete or continuous OA The random variable is discrete OB The random variable is continuous d Is the number of light bulbs that burn out in the next week in a room with 13 bulbs discrete or continuous OA The random variable is discrete OB The random variable is continuous e Is the number of people with blood type A in a random sample of 15 people discrete or continuous OA The random variable is continuous OB The random variable is discrete

A poll was conducted to investigate opinions about global warming The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming The results are given in the accompanying data table Use a 0 01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming Do men and women appear to agree or is there a substantial difference C Human activity Natural patterns Don t know 73 69 Male 144 159 Female Click here to view the chi square distribution table 296 319 Identify the null and alternative hypotheses The sex of the respondent and the choice for the cause of global warming are independent The sex of the respondent and the choice for the cause of global warming are dependent Ho H Compute the test statistic Round to three decimal places as needed Chi square distribution table Degrees of Freedom 1 22 3 4 5 6 7 8 9 O 0 995 0 010 0 072 0 207 0 412 0 676 0 989 1 344 1 735 CER 0 99 0 020 0 115 0 297 0 554 0 872 1 239 1 646 2 088 Area to the Right of the critical value 0 975 0 001 0 051 0 216 0 484 0 831 1 237 1 690 2 180 2 700 0 95 0 004 0 103 0 352 0 711 1 145 1 635 2 167 2 733 3 325 0 90 0 10 0 05 0 025 0 01 0 016 2 706 3 841 5 024 6 635 0 211 4 605 5 991 7 378 9 210 0 584 6 251 7 815 9 348 11 345 11 143 13 277 1 064 7 779 9 488 1 610 9 236 11 071 12 833 15 086 2 204 10 645 12 017 13 362 15 507 14 684 16 919 12 592 14 449 16 812 14 067 16 013 18 475 17 535 20 090 19 023 21 666 2 833 3 490 4 168 X 0 005 7 879 10 597 12 838 14 860 16 750 18 548 20 278 21 955 23 589

The table below includes results from polygraph lie detector experiments conducted by researchers In each case it was known if the subjected lied or did not lie so the table indicates when the polygraph test was correct Use a 0 05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication Do the results suggest that polygraphs are effective in distinguishing between truth and lies Click the icon to view the table Determine the null and alternative hypotheses OA Ho Polygraph testing is accurate H Polygraph testing is not accurate OB Ho Whether a subject lies is not independent of the polygraph test indication H Whether a subject lies is independent of the polygraph test indication O Ho Whether a subject lies is independent of the polygraph test indication H Whether a subject lies is not independent of the polygraph test indication Ho Polygraph testing is not accurate H Polygraph testing is accurate M Determine the test statistic x 9 925 Round to three decimal places as needed Determine the P value of the test statistic P value 0 0016 Round to four decimal places as needed Do the results suggest that polygraphs are effective in distinguishing between truth and lies OA There is sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication OB There is sufficient evidence to warrant rejection of the claim that polygraph testing is 95 accurate ufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication 05 Sourate

Tobias takes a sample of 20 different gender married couples In his sample he found that the husband was 147 68 millimeters taller on average and differences in the husband s and wife s heights had a standard deviation of 85 94 millimeters Calculate a 95 confidence interval for the mean difference between husband height and wife height Write your answers to two decimal places Confidence interval Hd

Many universities use a student s ACT score to help with admission decisions as well as placement decisions ACT Score 16 18 24 26 28 30 32 GPA 2 2 5 3 4 4 5 5 5 2 3 5

The table below includes results from polygraph lie detector experiments conducted by researchers In each case it was known if the subjected lied or did not lie so the table indicates when the polygraph test was correct Use a 0 05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication Do the results suggest that polygraphs are effective in distinguishing between truth and lies Click the icon to view the table Determine the null and alternative hypotheses OA Ho Polygraph testing is accurate H Polygraph testing is not accurate OB Ho Whether a subject lies is not independent of the polygraph test indication H Whether a subject lies is independent of the polygraph test indication C Ho Whether a subject lies is independent of the polygraph test indication H Whether a subject lies is not independent of the polygraph test indication OD Ho Polygraph testing is not accurate H Polygraph testing is accurate Determine the test statistic 9 925 Round to three decimal places as needed Determine the P value of the test statistic P value Round to four decimal places as needed COOR More Info Polygraph test indicated that the subject lied Polygraph test indicated that Did the Subject Actually Lie No Did Not Lie Yes Lied 26 14 X

Conduct the hypothesis test and provide the test statistic and the critical value and state the conclusion A person randomly selected 100 checks and recorded the cents portions of those checks The table below lists those cents portions categorized according to the indicated values Use a 0 10 significance level to test the claim that the four categories are equally likely The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category but do the results support that expectation Cents portion of check Number Click here to view the chi square distribution table 0 24 31 25 49 24 The test statistic is 2 16 Round to three decimal places as needed The critical value is 6 251 Round to three decimal places as needed State the conclusion 50 74 21 Ho There claim that the four categories are equally likely The results support the expectation that the frequen 75 99 24 sufficient evidence to warrant rejection of the to 0

The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades Using this data consider the equation of the regression line bo b x for predicting the midterm exam grade that a student will earn based on the number of hours spent studying Keep in mind the correlation coefficient may or may not be statistically significant for the data given Remember in practice it would not be appropriate to use the regression line to make a prediction If the correlation coefficient is not statistically significant Hours Studying 1 2 3 4 5 Midterm Grades 75 79 87 88 94 Table Copy Data

Consider the relationship between the number of bids an item on eBay received and the item s selling price The following is a sample of 5 items sold through an auction Price in Dollars 29 32 41 44 47 Number of Bids 10 12 13 14 18 Step 3 of 3 Calculate the correlation coefficient r Round your answer to three decimal places Copy Data

best for quality family time Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected The table below shows goodness of fit test results from the claim and data from the study Test that claim using either the critical value method or the P value method with an assumed significance level of 0 05 Num Categories 7 Degrees of freedom 6 Expected Freq 113 0000 Test statistic x Critical x P Value 9 296 12 592 0 1576 Determine the null and alternative hypotheses Ho All days of the week have an equal chance of being selected H At least one day of the week has a different chance of being selected Identify the test statistic x Type an integer or a decimal

Conduct the hypothesis test and provide the test statistic and the critical value and state the conclusion A person randomly selected 100 checks and recorded the cents portions of those checks The table below lists those cents portions categorized according to the indicated values Use a 0 10 significance level to test the claim that the four categories are equally likely The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category but do the results support that expectation Cents portion of check Number 25 49 24 Click here to view the chi square distribution table 0 24 31 The test statistic is Round to three decimal places as needed 50 74 21 Degrees of Freedom 1 Chi square distribution table 2 3 4 5 6 7 8 75 99 24 9 10 0 995 D 0 010 0 072 0 207 0 412 0 676 0 989 1 344 1 735 2 156 0 99 SWAN 0 020 0 115 0 297 0 554 0 872 1 239 1 646 2 088 2 558 Area to the Right of the Critical Value 0 975 0 001 0 051 0 216 0 484 0 831 1 237 1 690 2 180 2 700 3 247 0 95 0 004 0 103 0 352 0 711 1 145 1 635 2 167 2 733 3 325 3 940 0 90 0 016 0 211 0 584 1 064 1 610 2 204 2 833 3 490 4 168 4 865 0 10 0 05 0 01 6 635 2 706 3 841 4 605 5 991 9 210 6 251 7 815 11 345 7 779 9 488 13 277 9 236 11 071 12 833 15 086 10 645 12 592 14 449 16 812 12 017 14 067 13 362 15 507 16 013 18 475 17 535 20 090 16 919 19 023 21 666 14 684 15 987 18 307 20 483 23 209 0 025 5 024 7 378 9 348 11 143 0 005 7 879 10 597 12 838 14 860 16 750 18 548 20 278 21 955 23 589 25 188 X

In a study of high school students at least 16 years of age researchers obtained survey results summarized in the accompanying table Use a 0 05 significance level to test the claim of independence between texting while driving and driving when drinking alcohol Are those two risky behaviors independent of each other Click the icon to view the table of survey results Determine the null and alternative hypotheses Ho Texting while driving is independent of driving while drinking alcohol H Texting while driving and driving while drinking alcohol are dependent Determine the test statistic x Round to two decimal places as needed

The line graph to the right shows the average gasoline prices of a country from 1985 through 2010 Let p q and r represent the following simple statements p Prices peaked in 2005 q Prices remained steady from 1990 through 1995 r Prices were more than 1 00 per gallon in 1985 Write the symbolic statement pvr in words Then use the information given by the graph to determine the truth value of the statement Average Price per Gallon unleaded regular Average Gasoline Prices 4 00 3 00 2 00 1 00 0 00 Write the symbolic statement pvr in words Choose the correct sentence below 1990 A Prices peaked in 2005 or prices were more than 1 00 per gallon in 1985 B Prices did not peak in 2005 or were more than 1 00 per gallon in 1985 C Prices peaked in 2005 or prices were not more than 1 00 per gallon in 1985 D Prices did not peak in 2005 or prices were not more than 1 00 per gallon in 1985 2000 Year 2010 e

Investigate opinions about global warming The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming Th results are given in the accompanying data table Use a 0 01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming Do men and women appear to agree or is there a substantial difference Human activity Natural patterns Don t know 35 36 Male 147 Female 170 Click here to view the chi square distribution table 331 311 Identify the null and alternative hypotheses Ho The sex of the respondent and the choice for the cause of global warming are independent H The sex of the respondent and the choice for the cause of global warming are dependent Compute the test statistic Round to three decimal places as needed

Complete the truth table for the given statement by filling in the required columns pv q p T TFF q T F T F q pv q

The table below includes results from polygraph lie detector experiments conducted by researchers In each case it was known if the subjected lied or did not lie so the table indicates when the polygraph test was correct Use a 0 05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication Do the results suggest that polygraphs are effective in distinguishing between truth and lies Click the icon to view the table Determine the null and alternative hypotheses OA Ho Polygraph testing is accurate H Polygraph testing is not accurate OB Ho Polygraph testing is not accurate H Polygraph testing is accurate C Ho Whether a subject lies is independent of the polygraph test indication H Whether a subject lies is not independent of the polygraph test indication O D Ho Whether a subject lies is not independent of the polygraph test indication H Whether a subject lies is independent of the polygraph test indication Determine the test statistic x Round to three decimal places as needed More Info Polygraph test indicated that Did the Subject Actually Lie No Did Not Lie Yes Lied 35 X

An investigator analyzed the leading digits from 792 checks issued by seven suspect companies The frequencies were found to be 255 143 110 87 49 46 46 41 and 15 and those digits correspond to the leading digits of 1 2 3 4 5 6 7 8 and 9 respectively If the observed frequencies are substantially different from the frequencies expected with Benford s law shown below the check amounts appear to result from fraud Use a 0 01 significance level to test for goodness of fit with Benford s law Does it appear that the checks are the result of fraud Leading Digit Actual 1 2 3 4 5 6 7 8 9 255 143 110 87 49 46 46 41 15 Frequency Benford s Law 30 1 17 6 12 5 9 7 7 9 6 7 5 8 5 1 4 6 Distribution of Leading Digits Determine the null and alternative hypotheses Ho The leading digits are from a population that conforms to Benford s law H At least one leading digit has a frequency that does not conform to Benford s law Calculate the test statistic x x Round to three decimal places as needed

Let p and q represent the following statements p 2 8 9 q 10 3 60 Determine the truth value for the statement p q Choose the correct truth value below Op q is false Op q is true

Complete the truth table for the given statement by filling in the required columns q p p q T T T F F F F p q p

The table below lists the number of games played in a yearly best of seven baseball championship series along with the expected proportions for the number of games played with teams of equal abilities Use a 0 05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions Games Played Actual contests Expected proportion 4 18 2 16 5 19 4 16 Determine the null and alternative hypotheses 6 20 5 16 7 36 5 16 Calculate the test statistic x x Round to three decimal places as needed n Ho The observed frequencies agree with the expected proportions H At least one of the observed frequencies do not agree with the expected proportion

Terri Vogel an amateur motorcycle racer averages 129 45 seconds per 2 5 mile lap in a 7 lap race with a standard deviation of 2 25 seconds The distribution of her race times is normally distributed We are interested in one of her randomly selected laps Source log book of Terri Vogel Let X be the number of seconds for a randomly selected lap Round all answers to 4 decimal places where possible a What is the distribution of X X N 129 45 2 25 b Find the proportion of her laps that are completed between 127 48 and 129 69 seconds 0 3518 c The fastest 3 of laps are under d The middle 60 of her laps are from seconds seconds to seconds

In a study of high school students at least 16 years of age researchers obtained survey results summarized in the accompanying table Use a 0 05 significance level to test the claim of independence between texting while driving an driving when drinking alcohol Are those two risky behaviors independent of each other Click the icon to view the table of survey results Determine the null and alternative hypotheses Ho H Texting while driving and driving while drinking alcohol are dependent Texting while driving is independent of all other risky behaviors Texting while driving is independent of driving while drinking alcohol Texting while driving and other risky behaviors are dependent Survey Results Texted While Driving Drove When Drinking Alcohol Yes No 733 3013 X

Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency tab Choose the correct answer below OA The null hypothesis is that the row and column variables are independent of each other B The number of degrees of freedom is r 1 c 1 where r is the number of rows and c is the number of columns C Tests of independence with a contingency table are always right tailed D Small values of the x test statistic reflect significant differences between observed and expected frequencies

Which of the following is NOT a requirement of conducting a hypothesis test for independence between the row variable and column variable in a contingency table Choose the correct answer below OA The sample data are randomly selected OB For every cell in the contingency table the observed frequency O is at least 5 OC The sample data are represented as frequency counts in a two way table OD For every cell in the contingency table the expected frequency E is at least 5

A case control or retrospective study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash Results given in the accompanying table Using a 0 05 significance level test the claim that injuries are independent of helmet color Color of Helmet Yellow 27 6 Black White 484 346 204 104 Controls not injured Cases injured or killed Click here to view the chi square distribution table Red 158 65 Identify the null and alternative hypotheses Choose the correct answer below OA Ho Whether a crash occurs and helmet color are independent H Whether a crash occurs and helmet color are dependent OB Ho Whether a crash occurs and helmet color are dependent H Whether a crash occurs and helmet color are independent OC Ho Injuries and helmet color are independent H Injuries and helmet color are dependent O D Ho Injuries and helmet color are dependent H Injuries and helmet color are independent Blue 85 40 Chi square distribution table Degrees of Freedom 1 2 3 4 5 6 7 8 9 0 995 0 010 0 072 0 207 0 412 0 676 0 989 1 344 1 735 0 99 Area to the Right of the Critical Value 0 975 0 001 0 020 0 051 0 115 0 216 0 297 0 484 0 554 0 831 0 872 1 237 1 239 1 690 1 646 2 180 2 088 2 700 0 95 0 90 0 004 0 016 0 103 0 211 0 352 0 584 0 711 1 064 1 145 1 610 1 635 2 204 2 167 2 833 2 733 3 490 3 336 4100 0 05 3 841 5 991 0 01 0 10 2 706 0 025 5 024 6 635 4 605 7 378 9 210 6 251 7 815 9 348 11 345 7 779 9 488 11 143 13 277 12 833 15 086 16 812 9 236 11 071 10 645 12 592 14 449 14 067 16 013 18 475 15 507 17 535 20 090 12 017 13 362 0 005 7 879 10 597 12 838 14 860 16 750 18 548 20 278 21 955

A poll was conducted to investigate opinions about global warming The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming The results are given in the accompanying data table Use a 0 01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming Do men and women appear to agree or is there a substantial difference Human activity Natural patterns Don t know 35 36 Male 147 170 Female Click here to view the chi square distribution table H 331 311 Identify the null and alternative hypotheses Ho and Vand Chi square distribution table Degrees of Freedom 1 2 3 4 5 6 7 8 0 995 0 99 0 975 0 001 0 051 Area to the Right of the critical value 0 010 0 020 0 072 0 115 0 216 0 207 0 484 0 297 0 412 0 554 0 831 0 676 0 872 0 989 1 239 1 344 1 646 1 237 1 690 2 180 Vare 0 95 0 90 0 004 0 016 0 103 0 211 0 352 0 584 0 711 1 145 1 635 2 167 2 733 are 1 064 1 610 2 204 2 833 3 490 0 10 2 706 4 605 6 251 7 779 9 236 10 645 12 592 12 017 14 067 13 362 15 507 0 05 3 841 5 991 7 815 9 488 11 071 0 025 0 01 5 024 6 635 7 378 9 210 9 348 11 345 11 143 13 277 12 833 15 086 14 449 16 812 16 013 17 535 18 475 20 090 X 0 005 7 879 10 597 12 838 14 860 16 750 18 548 20 278 21 955

ble below includes results from polygraph lie detector experiments conducted by researchers In each case was known if the subjected lied or did not lie so the table indicates when the polygraph test was correct Use a 0 05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication Do the results suggest that polygraphs are effective in distinguishing between truth and lies Click the icon to view the table Determine the null and alternative hypotheses OA Ho Polygraph testing is accurate H Polygraph testing is not accurate OB Ho Polygraph testing is not accurate H Polygraph testing is accurate OC Ho Whether a subject lies is independent of the polygraph test indication H Whether a subject lies is not independent of the polygraph test indication OD Ho Whether a subject lies is not independent of the polygraph test indication H Whether a subject lies is independent of the polygraph test indication ampl More Info Polygraph test indicated that the subject lied Polygraph test indicated that Did the Subject Actually Lie No Did Not Lie Yes Lied 13 35 X

An investigator analyzed the leading digits from 792 checks issued by seven suspect companies The frequencies wer found to be 255 143 110 87 49 46 46 41 and 15 and those digits correspond to the leading digits of 1 2 3 4 5 6 7 8 and 9 respectively If the observed frequencies are substantially different from the frequencies expected with Benford s law shown below the check amounts appear to result from fraud Use a 0 01 significance level to test for goodness of fit with Benford s law Does it appear that the checks are the result of fraud Leading Digit Actual Frequency Benford s Law Distribution of Leading Digits Determine the null and alternative hypotheses Ho 1 255 30 1 H 2 3 4 5 6 143 110 87 49 46 17 6 12 5 9 7 7 9 6 7 At most three leading digits have frequencies that do not conform to Benford s law At least one leading digit has a frequency that does not conform to Benford s law At least two leading digits have frequencies that do not conform to Benford s law The leading digits are from a population that conforms to Benford s law 7 46 5 8 8 41 5 1 9 15 4 6 L

The table below lists the number of games played in a yearly best of seven baseball championship series along with the expected proportions for the number of games played with teams of equal abilities Use a 0 05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions Games Played Actual contests Expected proportion Ho 4 18 2 16 Determine the null and alternative hypotheses H 5 19 4 16 6 20 5 16 7 36 5 16 The observed frequencies agree with the expected proportions At least one of the observed frequencies do not agree with the expected proportions The observed frequencies agree with two of the expected proportions The observed frequencies agree with three of the expected proportions

Fill in the blank In a In a we test the claim that different populations have the same proportions of some characteristics two way analysis of variance test of homogeneity we test the claim that different populations have the same proportions of some characteristi McNemar s test

the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected The table below shows goodness of fit test results from the claim and data from the study Test that claim using either the critical value method or the P value method with an assumed significance level of a 0 05 Num Categories Degrees of freedom Expected Freq Ho 7 6 H 113 0000 Test statistic Determine the null and alternative hypotheses Critical x P Value 9 296 12 592 0 1576 All days of the week have an equal chance of being selected All days of the week have a different chance of being selected At least two days of the week have a different frequency of being selected At least one day of the week has a different chance of being selected

The table below lists leading digits of 317 inter arrival Internet traffic times for a computer along with the frequencies of leading digits expected with Benford law When using these data to test for goodness of fit with the distribution described by Benford s law identify the null and alternative hypotheses Leading Digit Benford s Law Leading Digits of Inter Arrival Traffic Times 2 3 4 5 6 7 8 9 1 30 1 17 6 12 5 9 7 7 9 6 7 5 8 5 1 4 6 76 62 Choose the correct answer below 29 33 19 27 28 OA Ho None of the proportions are equal to the given claimed value H P 0 301 and p2 0 176 and p3 0 125 and and pg 0 046 OB Ho P 0 301 and p2 0 176 and p3 0 125 and and pg 0 046 H At least one of the proportions is different from the others 21 OC Ho At least one of the proportions is not equal to the given claimed value H P 0 301 and p 0 176 and p3 0 125 and and pg 0 046 O D Ho P 0 301 and p 0 176 and p3 0 125 and and pg 0 046 H At least one of the proportions is not equal to the given claimed value OE Ho At least one of the proportions is different from the others He 0301 and p 0176 and n 0 125 22

A is a table in which frequencies correspond to two variables is a table in which frequencies correspond to two variable Pearson correlation coefficient table contingency table standard normal distribution table

Terri Vogel an amateur motorcycle racer averages 129 45 seconds per 2 5 mile lap in a 7 lap race with a standard deviation of 2 25 seconds The distribution of her race times is normally distributed We are interested in one of her randomly selected laps Source log book of Terri Vogel Let X be the number of seconds for a randomly selected lap Round all answers to 4 decimal places where possible a What is the distribution of X X NO 129 45 2 25 b Find the proportion of her laps that are completed between 127 48 and 129 69 seconds 0 3518 c The fastest 3 of laps are under d The middle 60 of her laps are from seconds seconds to seconds

The 1 in 6 wins game As a special promotion for its 20 ounce bottles of soda a soft drink company printed a message on the inside of each bottle cap Some caps said Please try again while others said You re a winner The company advertised the promotion with the slogan 1 in 6 wins a prize Seven friends each buy one 20 ounce bottle at a local convenience store The store clerk is surprised when three of them win a prize Is this group of friends just lucky 3 out of 7 winners could happen by chance or is the company s 1 in 6 claim inaccurate 3 out of 7 winners is not likely to happen by chance First perform a simulation to help answer this question For now let s assume that the company is telling the truth and that every 20 ounce bottle of soda it fills has a 1 in 6 chance of getting a cap that says You re a winner 1 How can we model this 2 Define and conduct one trial for this simulation

Look at the two histograms below Each involves the same number of data The data are all whole numbers so the height of each bar represents the number of values equal to the corresponding midpoint sho horizontal axis Notice that both distributions are symmetric 0 Frequency 4 5 6 7 8 9 10 a Estimate the mode median and mean for each histogram 4 3 2 1 0 mode median mean b Which distribution has the larger standard deviation Why O Distribution 1 because more of the data are farther from the mean O Distribution i because more of the data are farther from the mean O Distribution 1 because more of the data are closer to the mean O Distribution II because more of the data are closer to the mean 4 5 6 7 8 9 10