Ap stats 9-12

Which of the following describes a Type II error in this setting? (a) Not finding convincing evidence that the mean pulse rate of agricultural students is greater than 72 bpm when in fact the mean pulse rate of agricultural students is greater than 72 bpm. (b) Not finding convincing evidence that the mean pulse rate of agricultural students is 80 bpm when in fact the mean pulse rate of agricultural students is 72 bpm. (c) Finding convincing evidence that the mean pulse rate of agricultural students is greater than 72 bpm when, in fact, the mean pulse rate of agricultural students is less than 72 bpm. (d) Finding convincing evidence that the mean pulse rate of agricultural students is greater than 72 bpm when in fact the mean pulse rate of agricultural students is 72 bpm. (e) Finding convincing evidence that the mean pulse rate of agricultural students is greater than 72 bpm when in fact the mean pulse rate of agricultural students is greater than 72 bpm.

(a) Not finding convincing evidence that the mean pulse rate of agricultural students is greater than 72 bpm when in fact the mean pulse rate of agricultural students is greater than 72 bpm.

A test of significance produces a P-value of 0.024. Which of the following conclusions is appropriate? (a) Reject Ho at the a = 0.05 level (b) Accept Ha at the a = 0.05 level (c) Reject Ha at the a = 0.01 level (d) Accept Ho at the a = 0.01 level (e) Fail to reject Ho at the a = 0.05 level

(a) Reject Ho at the a = 0.05 level

Which of the following is an appropriate interpretation of the number 0.092498? (a) For each increase of $100,000 in profits, the predicted sales increases by $9,249.80. (b) For each increase of $100,000 in sales, the predicted profit increases by $9,249.80 (c) Sales of $100,000 correspond to predicted average profits of $9,249.80. (d) The actual profit typically varies by about $9249.80 from the profit predicted with the least squares regression line using x = sales. (e) The actual sales typically varies by about $9249.80 from the sales predicted with the least squares regression line using r= profit.

(b) For each increase of $100,000 in sales, the predicted profit increases by $9,249.80

A 95% confidence interval for the proportion of viewers of a certain reality television show who are over age 30 is (0.26, 0.35). The show's producers want to test the hypothesis H, : p = 0.25 against H: p+ 0.25. Which of the following is an appropriate conclusion for them to draw? (a) Reject H, at both a = 0.01 and a = 0.05. (b) Reject H, at a =0.05. (c) Fail to reject H at a = 0.05 but reject at a = 0.01 . (d) Reject H, at a = 0.10, fail to reject for any smaller a level. (e) The producers do not have enough information to perform a test of significance.

(b) Reject H, at a =0.05.

Which of the following conditions must be met in order to use at procedure on these paired data? (a) The distribution of before-diet weights must be approximately Normal. (b) The distribution of differences (before - after) must be approximately Normal. (c) The distribution of both before-diet weights and after-diet weights must be approximately Normal (d) The distribution of before-diet weights and the distribution of differences (before - after) must be approximately Normal. (e) All three distributions of weight (before-diet, after-diet, and the differences) must be approximately Normal.

(b) The distribution of differences (before - after) must be approximately Normal.

You are thinking of using at procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct? (a) You should not use the t procedure because the population does not have a Normal distribution. (b) You may use the t procedure as long as your sample size is at least 30. (c) You may use the t procedure, but you should probably claim only that the significance level is 0.10. (d) You may not use the t procedure unless the sample size is less than 30. (e) You may use the t procedure as long as there are no outliers.

(b) You may use the t procedure as long as your sample size is at least 30.

A test of H, : u = 60 versus H, : u ‡ 60 based on a sample mean of 7 = 58 yields a P-value of 0.04. Using a = 0.05, which of the following is an appropriate conclusion? (a) There is sufficient evidence to conclude that u < 60. (b) There is sufficient evidence to conclude that u = 60 (c) There is sufficient evidence to conclude that u ‡ 60. (d) There is insufficient evidence to conclude that u ‡ 60. (e) There is insufficient evidence to conclude that u = 60.

(c) There is sufficient evidence to conclude that u ‡ 60.

A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. She will only accept the shipment if there is convincing evidence that this proportion is less than 0.06. She selects a random sample of 50 apples from the over 20,000 apples on the truck to test the hypotheses Ho: p = 0.06, H.: p <0.06. Which of the following conditions for inference have not been met in this situation? (a) The data are a random sample from the population of interest. (k) The sample size is less than 10% of the population size. (c) np ≥ 10 and n(1- p) ≥ 10 (d) The population distribution is approximately Normal. (e) More than one condition is violated.

(c) np ≥ 10 and n(1- p) ≥ 10

Mrs. Peterson claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you've been keeping track. In the past 80 selections, the number "five" has come up only 8 times. You suspect that the calculator is producing fewer fives than it should. Let p = the true long-run proportion of five's produced by the calculator. What is the approximate P-value for this test? (a) -2.24 (6) -2.98 (a) 0.0028 (d) 0.0127 (e) 0.0250

(d) 0.0127

A test of the null hypothesis H, :4 = 0 against the alternative H, : u +0 produces the test statistic t=2.808. If the sample size is n= 10, which of the following intervals contains the P-value? (a) P < 0.005 (b) 0.005 < P< 0.01 (c) 0.01 < P < 0.02 (d) 0.02 < P < 0.05 (e) 0.05 < P < 0.10

(d) 0.02 < P < 0.05

Which of the following is an appropriate alternative hypothesis for addressing this question? (a) The observed number of drivers choosing each lane is equal. (b) The observed number of drivers choosing each lane is different from the expected numbers. (c) The proportions of drivers choosing each of the three lanes are equal. (d) Drivers are not equally likely to choose each of the three lanes. (e) The proportions of drivers choosing each of the three lanes are all different.

(d) Drivers are not equally likely to choose each of the three lanes.

When checking the conditions for regression inference, which of the following is evidence that the condition of equal standard deviation of y for each value of x has not been satisfied? (a) The residual plot has a distinctly curved shape. (b) The residual plot shows a group of randomly scattered points. (c) The histogram of residuals is skewed to the right. (d) Small values of the explanatory variable are associated with small residuals, and large values of the explanatory variable are associated with large residuals. (e) The scatterplot has a distinctly curved shape.

(d) Small values of the explanatory variable are associated with small residuals, and large values of the explanatory variable are associated with large residuals.

Which of the following is an appropriate interpretation of the number 22.5012? (a) The actual number of students enrolled typically varies by about 22.5012 from the number predicted with the least squares regression line using r = number of burglaries. (b) The typical distance between the predicted burglaries and the least-squares regression line is about 22.5012. (c)) The typical distance between observed values for student enrollment and values for enrollment predicted by the regression equation is about 22.5012. (d) The actual number of burglaries typically varies by about 22.5012 from the number predicted with the least squares regression line using r = student enrollment. (e) The sum of the squared deviations between the observed number of burglaries and the number of burglaries predicted by the regression equation is about 22.5012.

(d) The actual number of burglaries typically varies by about 22.5012 from the number predicted with the least squares regression line using r = student enrollment.

An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female employees. Let pi = the proportion of all male employees at the company who hold this opinion and p2 = the proportion of all female employees at the company who hold this opinion. We want to test the hypotheses H, : P, - p, =0, H, : P, - p. >O. The P-value for this test is 0.0217. Which of the following is the correct conclusion using a = 0.01? (a) Reject Ho. We have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. (b) Reject Ho. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. (c) Accept Ho. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. (d) Accept Ha. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. (e) Fail to reject Ho. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.

(e) Fail to reject Ho. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.

What are the appropriate null and alternative hypotheses? (a) Ho:M = 72; H. M <72 (b) H,: 5 = 72; H. :* <72 (c) H,:u =80; H, : M = 72 (d) H, iT =80; H : 7 > 72 (e) Ho: M = 72; H,: M > 72

(e) Ho: M = 72; H,: M > 72

Which of the following statements about power are true? I. Power = 1 - P(Type II Error). I. An increase in sample size increases power IlI. A test with higher power is more likely to reject a false null hypothesis. (a) I only (b) Il only (c) I and II (d) I and III (e) I, IL, and III

(e) I, IL, and III

A political campaign manager wants to test the effectiveness of a new advertisement featuring Candidate X. The campaign manager takes a random sample of 300 voters before the ad goes on air and another random sample of 250 voters afterwards. 158 of the 300 voters in the "before" sample say they support Candidate X and 140 voters in the "after" sample say they support Candidate X. If p, = the proportion of all voters who support Candidate X after the ad is aired and P. = the proportion of all voters who support Candidate X before the ad is aired, which of the following is the correct standardized test statistic for H, : P, - Pe=0? 0.56-0.527 Z= (a) z= 0.542(0.458) 0.542(0.458) 250 300 (c) z (e) 7 0.56-0.527 10.56(0.44) 0.527(0.473) 250 300 0.56-0.527 0.542 (0.458) 550 0.56 - 0.527 0.527 (d) /0.56(0.44) 250 + 0.56-0.527 10.527(0.473) 300 10.56 + \ 250 300

B

Which of the following is the correct expression for the chi-square statistic in this situation? (a) x°= ( (137-155). (159-155) (169-155) 155 155 155 (b) x? (137-155) (159-155) (169-155) 137 159 169 (137-155)} (159-155)? (169-155) 173 155 155 155 (4) y°= (137-155)° (159-155) (169-155) + 137 159 169 (137-155) (159-155) (169-155)? (e) p? = + 465 465 465

C) (137-155)} (159-155)? (169-155) 173 155 155 155

We wish to test if the two varieties are significantly different in their mean carbohydrate content. Which of the following are the appropriate null and alternative hypotheses for this situation? (a)1lo:A1 =1s:H1o:A <As (）10:41=10;B1a:1二12 (HO:M=1s;HloA大A2 (d）日0：元三元;日：元＜石 (e)10：元二石;日。云大石

C. (HO:M=1s;HloA大A2

Which of the following expressions best represents the margin of error of a 90% confidence interval for the slope of the population regression line? (a) 1.701V0.0106 0.0106 (b) 1.645 V38 1.701(0.0106) (d) 1.6450.0106

C. 1.701(0.0106)

Assuming the conditions for inference were met, which of the following is the most appropriate conclusion to draw at the a = 0.05 level? (a) The test provides convincing evidence that the mean carbohydrate content of variety 1 is greater than variety 2. (b) The test provides convincing evidence that the mean carbohydrate contents of the two varieties are equal. (c) We accept Ha, variety 1 has a different mean carbohydrate content than variety 2. © 2020

E

Under the assumption that the null hypothesis is true, which of the following represents the expected count for male children who chose a blue toy? (58)(116) (58) (116) (34) (58) (a) (b) 34 236 (6) 134)(116) 236 236 (d) 8 (e 236

E

Which of the following statements about power are true? I. Power = 1 - P(Type Il Error). I. An increase in sample size increases power. Ill. A test with higher power is more likely to reject a false null hypothesis. (a) I only (b) II only (c) I and Il (d) I and III (eVI. II. and III

E ll and lll

Which of the following is the correct standardized test statistic for a test of the null hypothesis that the water diet has no effect on weight loss? 7=0 (a) z =13.638 7-0 (b) t=73.638 V4 173.75-166 75 (c) z= 46.56- 36.09- 4 + 4 173.75 -166.75 (d) t= 146.562 36.092 + 4 4 173.75-166.75 (e) t 46.56- 4 36.092

b) t=73.638 V4 173.75-166 75

Which of the following is the appropriate null hypothesis for this test? (a) The distribution of color preference is 25% for each color, regardless of gender. (b) Males are more likely to choose a blue toy and females are more likely to choose a pink toy. (c) The distribution of color preference is the same for male and female 12- to 18-month-old children. (d) Color preference is associated with gender in the population of 12- to 18-month old children. (e) Color preference is independent of gender in the population of 12- to 18-month old children.

c) The distribution of color preference is the same for male and female 12- to 18-month-old children.

The chi-square statistic for these data is y? = 8.134. Which of the following intervals contains the P-value for this test? (a) 0.005 < P - value < 0.01 (b) 0.01< P- value < 0.025 K(c)) 0.025 < P - value ≤ 0.05 Ta 0.05 < P - value < 0.1 (e) P- value > 0.1

c)) 0.025 < P - value

We want to know if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these. What is the P-value of this test? (a) 0.006 (b) 0.012 (c) 0.041 / (d) 0.082 (e) 0.164

d) 0.082

Mr. Mastrogiacomo is testing the hypothesis that the proportion of households in a large town that have high-speed internet service is equal to 0.7 against the alternative that the proportion is different from 0.7. What is the chief advantage of using a confidence interval to test this hypothesis rather than a significance test? (a) A confidence interval can be one-sided or two-sided but the significance test is always two-sided. (b) The conditions for using a confidence interval are less restrictive than for a significance test. (c) A confidence interval has more power than the significance test. ((d) A confidence interval gives a set of plausible values for the true proportion. (e) There is no advantage. A significance test should be used, not a confidence interval.

d) A confidence interval gives a set of plausible values for the true proportion.

Some people say that more babies are born in September than in any other month. To test this claim, you take a random sample of 150 students at your school and find that 21 of them were born in September. You are interested in whether the proportion born in September is greater than 1/12 what you would expect if September was no different from any other month. Thus, the null hypothesis is H, : p=1/12. The P-value for your test is 0.0056. Which of the following statements correctly interprets the P-value? (a) The probability that September birthdays are no more common than any other month is 0.0056. (b) The probability that September birthdays are more common than other months is 0.0056. (c) The probability that the proportion of September birthdays is not equal to 1/12 is 0.0056. (d) Assuming that the proportion of babies born in September is the same as any other month, there is a 0.0056 probability of getting a sample proportion of 21/150 or greater by chance alone. (e) Assuming that the proportion of babies born in September is greater than any other month, there is a 0.0056 probability of getting a sample proportion of 21/150 or greater by chance alone.

d) Assuming that the proportion of babies born in September is the same as any other month, there is a 0.0056 probability of getting a sample proportion of 21/150 or greater by chance alone.

A grocery store manager wants to know if displaying cranberries near the entrance to the store increases the proportion of shoppers who buy them. To determine this, the manager flips a coin each morning to decide whether to place the cranberries near the entrance that day or to locate them in the produce section. The manager takes a random sample of shoppers over several days and calculates p, = the proportion of shoppers who buy cranberries when they are near the store entrance, and p, = the proportion of shoppers Who buy cranberries when they are in the produce section. Which of the following is a correct set of hypotheses for the appropriate test of significance? (a) Hip=0; H : p#0 (b) Hip=0; H : p>0 (c) Ho:p, -p, =0; H : p -p, #0 (d) Ho: Pi- P. =0; H. : PI - Pa <0 (e) Vo : PI - P2 = 0; H. : P, - P. > 0

e) Vo : PI - P2 = 0; H. : P, - P. > 0