10-1, 10-2, 11-1, 11-2. 12-1

9) Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the ​p-value. Source DF SS MS F P Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

0.011

4) Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=102.15​, y=104.3​, r=0.897​, ​P-value=​0.000, and y=2.25+1x​, where x represents the IQ score of the twin born first. Find the best predicted value of y given that the twin born first has an IQ of 101​? Use a significance level of 0.05.

2.25+1(101) = y= 103.25

7) Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Find the critical value. Source DF SS MS F P Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80

4.07

8) Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the value of the test statistic. Source DF SS MS F P Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

5.17

3) Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01. Internet Users (Per 100) Award Winners 79.6 5.5 80.1 9.1 57.6 3.2 68.5 1.6 78.2 10.4 38.3 0.1

A: Construct a scatterplot. Choose the correct graph below. B: The linear correlation coefficient is r= 0.800 (round to three decimal places as needed.) C: Determine the null and alternative hypotheses. Ho: p= 0 H1: p ≠ 0 0.800/sqr 1-0.8*2/6-2 D: The test statistic is t= 2.66 (Round to two decimal places as needed.) E: The P-value is 0.056 (Round to three decimal places as needed.) F: Greater Than Is not

Use the given data set to complete parts (a) through (c) below (use a= 0.05) x y 10 7.47 8 6.78 13 12.74 9 7.12 11 7.81 14 8.84 6 6.08 4 5.39 12 8.14 7 6.43 5 5.74

A: Construct a scatterplot. Choose the correct graph below. B: Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= 0.817 (Round to three decimal places as needed.) C: Using the linear correlation coefficient found in the previous​ step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. There is sufficient evidence to support the claim of a linear correlation between the two variables. D: Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below. The scatterplot reveals a perfect straight-line pattern, except for the presence of one outlier.

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05. x y 10 7.47 8 6.77 13 12.74 9 7.12 11 7.81 14 8.84 6 6.09 4 5.39 12 8.14 7 6.42 5 5.73

A: Construct a scatterplot. Choose the correct graph below. Graph: number 4 across and up B: Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. 0.817 C: Using the linear correlation coefficient found in the previous​ step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. There is sufficient evidence to support the claim of a linear correlation between the two variables. D: Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below. The scatterplot reveals a perfect straight-line pattern, except for the presence of one outlier.

2) A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and​ glass? Use a significance level of α=0.05. Correlation​ matrix: Variables/ Paper/Glass Paper 1 0.1623 Glass 0.1623 1

A: Determine the null and alternative hypotheses. H1​: p = 0 H1: p ≠0 Paper/glass #: 0.162 B: Identify the test statistic, r. r= 0.162 C: Identify the critical value(s). (round to three decimal places as needed.) There are two critical values at r= +0.254 D: State the conclusion. Less than or equal to is not

2) In​ soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 291 kicks during games among top teams. In the​ table, jump direction indicates which way the goalkeeper​ jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.01 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so​ fast, goalkeepers have no time to​ react, so the directions of their jumps are independent of the directions of the​ kicks? _ Jump_Left Jump_Center Jump_Right Kick_Left 54 0 37 Kick_Center 42 14 32 Kick_Right 41 9 62

A: Ho: Jump direction is independent of kick direction. H1: Jump direction is dependent on kick direction. B: Determine the test statistic. x2= 24.361 (round to three decimal places as needed.) C: Determine the P-value of the test statistic. P-value= 0.0000 (round to four decimal places as needed) D: sufficient do not support

The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per​ year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the​ results, does the type of vehicle appear to affect the amount of greenhouse gas​ emissions? Type A Type B Type C 6.7 7.6 8.7 6.4 7.3 9.6 7.4 6.7 9.4 6.5 8.3 8.4 6.3 7.6 9.4 7.2 8.3 8.2 6.2 7.2 7.9 6.5 7.7 9.9 5.9 9.2 7.1

A: Ho: u1=u2=u3 H1: At least one of the means is different from the others. B: Determine the test statistic. F= 39.68 (Round to two decimal places as needed). C: Identify the P-value P-value= 0.00 (round to two decimal places as needed) D: What is the conclusion of the test? Reject Does

Refer to the accompanying data​ table, which shows the amounts of nicotine​ (mg per​ cigarette) in​ king-size cigarettes,​ 100-mm menthol​ cigarettes, and​ 100-mm nonmenthol cigarettes. The​ king-size cigarettes are​ nonfiltered, while the​ 100-mm menthol cigarettes and the​ 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the​ king-size cigarettes are not​ filtered, do the filters appear to make a​ difference? King-Size 100-mm_Menthol Filtered_100-mm_Nonmenthol 1.7 1.2 0.9 1.1 0.9 1.0 1.0 1.2 0.6 1.2 0.8 1.2 1.5 1.2 1.0 1.3 1.3 0.7 1.3 0.9 1.0 1.0 1.1 1.2 1.2 1.4 0.9 1.1 0.8 1.1

A: Ho: u1=u2=u3 H1: At least one of the three population means is different from the others B: Find the F test Statistic F= 4.4252 (Round to four decimal places as needed.) C: Find the P-value using F test statistic. P-value= 0.0218 D: What is the conclusion for this hypothesis test? Reject Ho. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. E: Do the filters appear to make a difference? Given that the king-size cigarettes have the largest mean, it appears that the filters do make difference (although this conclusion is not justified by the results from analysis of variance).

3) 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 0.05 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 Male 335 160 40 Female 353 151 41

A: Identify the null and alternative hypotheses. Ho: The sex of the respondent/ the choice for the cause of global warming/ independent H1: The sex of the respondent/ the choice for the cause of global warming/dependent B: Compute the test statistic. 0.649 (Round to three decimal places as needed.) C: Find the critical value(s) 5.991 (usually always same answer for all questions) D: What is the conclusion? Fail to reject is not appear

1) A random sample of 794 subjects was asked to identify the day of the week that is 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 α=0.05. Num Categories 7 Test​ statistic, χ2 252.977 Degrees of freedom 6 Critical χ2 12.592 Expected Freq 113.4286 ​P-Value

A: Identify the test statistic: 252.977 B: Identify the critical value. 12.592 C: State the conclusion: Reject Is Does not appear

3) A police department released the numbers of calls for the different days of the week during the month of​ October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis? Day Frequency Sun 152Mon 201Tues 225Wed 247Thurs 179Fri 215Sat 230

A: The null and alternative hypotheses Ho: Police calls occur with the same frequency on the different days of the week. H1: At least one day has a different frequency of calls than the other days. B: Calculate the test statistic, x2 x2= 30.734 (Round to three decimal places as needed.) C: Calculate the P-value P-value = 0.0000 (round to four decimal places as needed.) D: What is the conclusion for this hypothesis test? Reject Ho: There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls. E: What is the fundamental error with this analysis? Because October has 31 days, three of the days of the week occur more often than other days of the week.

5) An investigator analyzed the leading digits from 761 checks issued by seven suspect companies. The frequencies were found to be 4​, 19​, 4​, 62​, 234​, 400​, 10​, 17​, and 11​, 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:1 4 30.10%2 19 17.60%3 4 12.50%4 62 9.70%5 234 7.90%6 400 6.70%7 10 5.80%8 17 5.10%9 11 4.60%

A: The null and alternative hypotheses: Ho: The leading digits are from a population that conforms to Benford's law. H1: At least one leading digit has a frequency that does not conform to Benford's law. B: Calculatue the test statistic x2 x2= 3356.025 (Round to three decimal places as needed) C: Calculate the P-value: P-value= 0.0000 (Round to four decimal places as needed) D: State the conclusion Reject Is does appear

2) 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 0.05 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 0-24 57 25-49 20 50-74 12 75-99 11

A: The test statistic is 56.56 B: The critical value is 7.815 C: State the conclusion: Reject IS appear

1) Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 125 and a​ y-intercept of −391. Complete parts​ (a) and​ (b) below.

A: What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice. Ỳ = -391 + (125 ) x B: What does the symbol Ỳ represent? The symbol Ỳ represents the predicted value of price.

5) The data show the bug chirps per minute at different temperatures. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted​ value? Chirps in 1 min Temperature (°F) 987 82.5 765 65 961 82.5 836 70 879 74.6 1235 93.3

A: What is the regression equation? y= 21.00+0.0603x B: The best predicted temperature when a bug is chirping at 3000 chirps per minute is 201.9 C: What is wrong with this predicted​ value? Choose the correct answer below. It is unrealistically high. The value 3000 is far outside of the range of observed values.

2) Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 8 14.86 14 20.54 13 20.48 6 10.14 12 20.06 11 19.30 7 12.68 9 16.70 15 20.24 10 18.18 5 7.24

A: Y= 3.40 + 1.30x (Round to two decimal places as needed) B: Create a scatterplot of the data. Choose the correct graph below. C: Identify a characteristic of the data that is ignored by the regression line. The data has a pattern that is not a straight line.

3) One way analysis of variance is used to test for​ ________.

Equality of three or more population means

4) ANOVA requires usage of the​ ________ distribution.

F

5)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?

For every cell in the contingency table, the observed frequency, O, is at least 5.

5) Select an appropriate null hypothesis for a one way analysis of variance test.

Ho: u1 =u2= u3= u4

9) Paired sample data may include one or more​ ___________, which are points that strongly affect the graph of the regression line.

Influential points

10) In a test of weight loss​ programs, 136 subjects were divided such that 34 subjects followed each of 4 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.05 significance level to test the claim that the mean weight loss is the same for the different diets.

No, because the P-value is greater than the significance level

2) At the same time each​ day, a researcher records the temperature in each of three greenhouses. The table shows the temperatures in degrees Fahrenheit recorded for one week. What type of test would you use to test the claim that the average temperature is the same in each greenhouse at a 0.05 significance​ level? Greenhouse #1 Greenhouse #2 Greenhouse #3 73 71 67 72 69 63 73 72 62 66 72 61 68 65 60 71 73 62 72 71 59

One-way ANOVA

8) In a​ scatterplot, a(n)​ ______________ is a point lying far away from the other data points.

Outlier

10) For a pair of sample​ x- and​ y-values, the​ ______________ is the difference between the observed sample value of y and the​ y-value that is predicted by using the regression equation.

Residual

11) A​ ______________ is a scatterplot of the​ (x,y) values after each of the​ y-coordinate values has been replaced by the residual value y

Residual plot

6) In a​ ____________ we test the claim that different populations have the same proportions of some characteristics.

Test of homogeneity

7) What is the difference between the following two regression​ equations? y=b0+b1x

The first equation is for sample date; the second equation is for a population.

6) The test statistic for​ one-way ANOVA is equal to​ ________.

Variance between samples __________________________________ Variance within samples

1) In a test of weight loss​ programs, 198 subjects were divided such that 33 subjects followed each of 6 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.05 significance level to test the claim that the mean weight loss is the same for the different diets. Source of Variation SS df MS F ​P-value F crit Between Groups 399.246 5 79.84922 2.4104 0.037938 2.261138 Within Groups 6360.376 192 33.12696 Total 6759.622 197

Yes, because the P-value is less than the significance level.