# mathematics

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces. A. The z of – 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. B. The z of – 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. C. The z of – 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. D. The z of – 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. Question 2 of 40 2.5 Points In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes. A. With a z of -1.2 there is sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes. B. With a P-value of 0.2302 there is not sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes. C. With a P-value of 0.2302 there is sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes. D. With a z of –1.2 there is not sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes. At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described. A. Ho: µ = 18.4 hours H a : µ ¹ 18.4 hours B. Ho: µ = 18.4 hours H a : µ < 18.4 hours C. Ho: µ ³ 18.4 hours H a : µ [removed] 18.4 hours The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply. A. All games played by the team in question in which the attendance is over 4000 B. All future home games to be played by the team in question C. All home games played by the team in question D. None of the populations given are appropriate A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis? A. 1.12 B. 1.48 C. 1.84 D. 2.15 A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis? A. 97.5% B. 5% C. 2.5% D. 95% A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply. A. The population is all shy workers. B. The population cannot be identified from the description of the study. C. The population is all American workers. D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like.. In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: H0 : µ = 9.8 hours Ha : µ > 9.8 hours Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased. A. Type I error B. Type II error C. Correct decision D. Can not be determined from this information A study of a brand of “in the shell peanuts” gives the following results: A significant event at the 0.01 level is a fan getting a bag with how many peanuts? A. 30 peanuts B. 25 or 30 peanuts C. 25 or 55 peanuts D. 25 peanuts The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by s = $13,700. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply. A. The current seventh graders at the principal’s school B. Seventh graders’ families at the school with a standard deviation of $13,700 C. All of the families of the class of seventh graders at the principal’s school D. All seventh graders’ families In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: H0 : µ = 8.0 hours Ha : µ > 8.0 hours Explain the meaning of a Type II error. A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hours B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ > 8.0 hours C. Concluding that µ > 8.0 hours D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours A poll of 1,068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat. A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats. B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats. C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats. D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.