Exam 9: Hypothesis Tests

The practice of concluding "do not reject H₀" is preferred over "accept H₀" when we

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. -At a certain manufacturing plant, a machine produced ball bearings that should have a diameter of 0.50 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 30 ball bearings to test to see if the process is "out of control" (i.e. to test to see if the average diameter differs from 0.50 mm). a.State the hypotheses associated with the manager's test. b.Describe a Type I error for this situation. c.Describe a Type II error for this situation.

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. -A fast food restaurant is considering a promotion that will offer customers to purchase a toy featuring a cartoon movie character. If more than 20% of the customers purchase the toy, the promotion will be profitable. A sample of 50 restaurants is used to test the promotion. a.State the hypotheses associated with the restaurant's test. b.Describe a Type I error for this situation. c.Describe a Type II error for this situation.

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. -Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is

Exhibit 9-1 -Refer to Exhibit 9-1. The p-value is

As a general guideline, the research hypothesis should be stated as the

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. -The average gasoline price of one of the major oil companies has been $3.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $3.06. Assume that the standard deviation of the population ( $\sigma$ ) is $0.09. a.State the null and the alternative hypotheses. b.Test the claim at $\infty$ = .05. c.What is the p-value associated with the above sample results?

Exhibit 9-2 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. The population standard deviation is known to be 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 9-2. The p-value is

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds that 6 parts are defective. Is this sufficient evidence to reject the entire shipment? Use a .05 level of significance to conduct the appropriate hypothesis test.

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance t =

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

You are given the following information obtained from a random sample of 4 observations. At a .05 level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.)

Identify the null and alternative hypotheses for the following problems. a.The manager of a restaurant believes that it takes a customer no more than 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.

A two-tailed test is performed at a 5% level of significance. The p-value is determined to be 0.09. The null hypothesis

A national poll reported that 58% of those with Internet access have made purchases online. To investigate whether this percentage applies to its own state, a legislator commissions a study. A random sample of 400 state residents who have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample provide sufficient evidence to conclude that the state differs from the nation with respect to making purchases online? Use the p-value to conduct the hypothesis test and use a .05 level of significance.

Exhibit 9-2 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. The population standard deviation is known to be 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 9-2. The test statistic is

Laura Naples, Manager of Heritage Inn, periodically collects and tabulates information about a sample of the hotel's overnight guests. This information aids her in pricing and scheduling decisions she must make. The table below lists data on ten randomly selected hotel registrants, collected as the registrants checked out. The data listed are: $\bullet$ Number of people in the group $\bullet$ Hotel's shuttle service used: yes or no $\bullet$ Total telephone charges incurred $\bullet$ Reason for stay: business or personal a. Before cell telephones became so common, the average telephone charge per registered group was at least $5.00. Laura suspects that the average has dropped. Test H₀: $\mu$ > 5 and H_a: $\mu$ < 5 using a .05 level of significance. Use both the critical value and p-value approaches to hypothesis testing. b. In the past, Laura has made some important managerial decisions based on the assumption that the average number of people in a registered group is 2.5. Now she wonders if the assumption is still valid. Test the assumption with a = .05 and use both the critical value and p-value approaches.