Hypothesis Testing (264 problems)

A cigarette manufacturer wants to test the claim that the variance of the nicotine content of its cigs. is 0.644 milligram. Assume that it is normally distributed. A sample of 20 cigs. has a std. dev. of 1.00 milligram. At a = 0.05, is there ample evidence to reject the manufacturer's claim?

Test at the .01 level claim that population variance is less than 158 if a sample of 10 had a variance of 164. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.

A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation.

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.2 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 5.9 minutes. Use a 0.05 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

A random sample of n = 12 is drawn from a population that is normally distributed, and sample variance is s² = 19.3. Use α = 0.025 in testing HO: ơ² ≤ 9.4 versus H1: ơ² > 9.4.

A manufacturer wants to know if the variance of their product is 84 if a sample of 28 had a variance of 79. Test the claim at the .05 level.

State the hypotheses and identify the claim, find the critical value(s), compute the test value, and make the decision, summarize the results.

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.2 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 5.9 minutes. Use a 0.05 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

For randomly selected adults, IQ scores are normally distributed with a standard deviation of 16. The scores of 15 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 16. HINT: calculate s for the 15 college students listed below.

A manufacturer wants to know if the variance of their product is 84 if a sample of 28 had a variance of 79. Test the claim at the .05 level.

State the hypotheses and identify the claim, find the critical value(s), compute the test value, and make the decision, summarize the results.

The Pittsburgh Police department claims that the standard deviation of the number of tickets they issue is 15 tickets. A police officer does not agree, and randomly selects the records of 14 officers. He finds the sample standard deviation to be 13.43 tickets. Assuming that the data is normally distributed, test the department’s claim using a = 0.01. Use the Chi-square test.

Test at the .01 level claim that population variance is less than 158 if a sample of 10 had a variance of 164. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.

A random sample of 51 observations was selected from a normally distributed population. The sample mean was = 88.6, and the sample variance was s² = 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.

Items sorted correctly by light marijuana users: n=64, x=53.5, s= 3.6

Items sorted correctly by heavy marijuana users: n=65, x=51.3, 4.5

A high school offers two identical math classes at 1pm, taught by two different teachers (Mr. A and Mr. B). The class material (lecture notes, study aids, test questions, etc) are identical for the two sections of the course. The students were assigned to these two classes randomly, and the students’ grades are normally distributed. The high school principal is interested in testing the consistency of the grading performed by each teacher. She collects the marks recorded for the class midterm, and discovers that in Mr. A’s class of 31 students, the average grade was 68% and the standard deviation was 16%. In Mr. B’s class of 30 students, the average grade was 70% with a standard deviation of 14%. Conduct a hypothesis test (α = 0.05) to determine if there is a significant difference in the variance between the grades submitted by the two teachers.

Consumer advocate claims there is no difference in variance of number of hours that 2 companies' batteries will last. Sample of 10 batteries selected from company x, and the variance of hours is 24. Sample of 10 batteries from company y has a variance of 40. At a significance level of 0.10, test the claim that there is no difference in the variance of the life of the batteries.

Consumer advocate claims there is no difference in variance of number of hours that 2 companies' batteries will last. Sample of 10 batteries selected from company x, and the variance of hours is 24. Sample of 10 batteries from company y has a variance of 40. At a significance level of 0.10, test the claim that there is no difference in the variance of the life of the batteries.

A researcher doing a fast food study claimed that the variance of the carbohydrate content of grilled chicken sandwiches at Arby’s is higher than the variance of the carbohydrate content of grilled chicken sandwiches at McDonald’s. The sample statistics are given below. Follow the guidelines on page 536 in our textbook, and test the researcher’s claim using the F-test with a = 0.05.

A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.

A large discount chain compares the performance of its credit managers in Ohio and Illinois by comparing the mean dollar amounts owed by customers with delinquent charge accounts in these two states. Two random samples of 10 delinquent accounts are selected from all delinquent accounts in Ohio and Illinois. The sample of Ohio gives a mean dollar amount of $524 with a standard deviation of $68. The second sample from Illinois yields a mean dollar amount of $473 with a standard deviation of $22. (i) Calculate a 95% confidence interval for the difference between the mean dollar amounts owed in Ohio and Illinois; (ii) Can we conclude at a 5% level of significance that there is a difference between the mean dollars owed by customers with delinquent charge accounts in Ohio and Illinois?

A medicine is effective only if the concentration of a certain chemical in it is at least 200 parts per million (ppm). At the same time, the medicine would produce an undesirable side effect if the concentration of the same chemical exceeds 200 ppm. How would you set up the null and alternative hypothesis to test the concentration of the chemical in the medicine?