Exam 9: Hypothesis Tests

Consider the following hypothesis test: H_o: $\mu$ 14 H_a: $\mu$ < 14 A sample of 64 provides a sample mean of 13 and a sample standard deviation of 4. a.Determine the standard error of the mean. b.Compute the value of the test statistic. c.Determine the p-value; and at 95% confidence, test the above hypotheses.

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let $\alpha$ = .05. a.State the null and the alternative hypotheses. b.Compute the test statistic. c.Using the p-value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. a.Determine the mean and the standard deviation. b.At 99% confidence using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed. c.Repeat the test using the p-value approach.

Consider the following hypothesis test: H_o: $\mu$ 38 H_a: $\mu$ > 38 You are given the following information obtained from a random sample of six observations. Assume the population has a normal distribution. a.Compute the mean of the sample b.Determine the standard deviation of the sample. c.Determine the standard error of the mean. d.Compute the value of the test statistic. e.At 95% confidence using the p-value approach, test the above hypotheses.

A student believes that the average grade on the statistics final examination was 87. A sample of 36 final examinations was taken. The average grade in the sample was 83.96 with a standard deviation of 12. a.State the null and alternative hypotheses. b.Using the critical value approach, test the hypotheses at the 5% level of significance. c.Using the p-value approach, test the hypotheses at the 5% level of significance.

The critical value of t for a two tail test with 6 degrees of freedom is

The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. At 95% confidence test to determine if there has been a significant decrease in the average price homes. a.State the null and alternative hypotheses to be tested. b.Compute the test statistic. c.Determine the critical value for this test. d.What do you conclude? e.Compute the p-value.

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. -Refer to Exhibit 9-4. The test statistic is

A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000. a.Develop the appropriate hypotheses for this problem. b.Compute the test statistic. c.Compute the p-value. d.Using the p-value approach at 95% confidence, test the above hypotheses. e.Using the critical value approach at 95% confidence, test the hypotheses.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

Exhibit 9-9 The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day. From past information, it is known that the standard deviation of the population is $1,200. -Refer to Exhibit 9-9. The value of the test statistic is

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population ( ) is $0.14. -Refer to Exhibit 9-8. The p-value for this problem is

In a lower one-tail hypothesis test situation, the p-value is determined to be 0.2. If the sample size for this test is 51, the t statistic has a value of

If a hypothesis is rejected at the 5% level of significance, it

Exhibit 9-3 n = 49 = 54.8 s = 28 H₀: $\mu$ 50 H_a: $\mu$ > 50 -Refer to Exhibit 9-3. The test statistic is

For the following hypothesis test, H_o: $\mu$ = 150 H_a: $\mu$ < 150 The test statistic

Identify the null and alternative hypotheses for the following problems. a.The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch. b.Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar. c.It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.

In order to test the following hypotheses at an $\alpha$ level of significance H₀: $\mu$ 800 H_a: $\mu$ > 800 The null hypothesis will be rejected if the test statistic Z is