Exam 9: Hypothesis Tests

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

"D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, it is believed that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a.Formulate the hypotheses for this problem. b.Compute the test statistic. c.What is the p-value associated with the sample results? What is your conclusion based on the p-value? Let $\alpha$ = .05.

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t =

An automobile manufacturer stated that it will be willing to mass produce electric-powered cars if more than 30% of potential buyers indicate they will purchase the newly designed electric cars. In a sample of 500 potential buyers, 160 indicated that they would buy such a product. a.State the hypotheses for this problem b.Compute the standard error of . c.Compute the test statistic. d.At 95% confidence, what is your conclusion? Should the manufacturer produce the new electric powered car?

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. -Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the critical value approach and the sample information reported below, carry out a test of this statement. Let $\alpha$ = 0.05.

If a hypothesis test leads to the rejection of the null hypothesis,

For a one-tailed test (lower tail) at 89.8% confidence, Z =

The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2012 was $110,000. A sample of 81 dentists, which was taken in 2013, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists's incomes in 2013 is $36,000. a.We want to test to determine if there has been a significant increase in the average yearly income of dentists. Provide the null and the alternative hypotheses. b.Compute the test statistic. c.Determine the p-value; and at 95% confidence, test the hypotheses.

Exhibit 9-1 n = 36 = 24.6 S = 12 H₀: $\mu$ 20 H_a: $\mu$ > 20 -Refer to Exhibit 9-1. The test statistic is

An assumption made about the value of a population parameter is called a

A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

The power curve provides the probability of

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population ( $\alpha$ ) is known to be 5.6 days. a.State the null and alternative hypotheses. b.Using the critical value approach, test to determine if their advertisement is legitimate. Let $\alpha$ = .05. c.Using the p-value approach, test the hypotheses at the 5% level of significance.

A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126. a.Formulate the hypotheses that can be used to determine whether the mean of all account balances is significantly different from $1,150. b.Compute the test statistic. c.Using the p-value approach, what is your conclusion? Let $\alpha$ = .05.

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 correct null hypothesis for this problem is

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five 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 80%. -Refer to Exhibit 9-5. The test statistic is

In 2012, seventy percent of Canadian households had an internet connection. A sample of 484 households taken in 2013 showed that 75% had an internet connection. We are interested in determining whether or not there has been a significant increase in the percentage of the Canadian households that have internet connections. a.State the null and alternative hypotheses to be tested. b.Compute the test statistic. c.The null hypothesis is to be tested at 95% confidence. Determine the critical value(s) for this test. d.What do you conclude?

For a one-tailed test (upper tail) at 93.7% confidence, Z =