Exam 9: Hypothesis Tests

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. At 95% confidence, it can be concluded that the mean of the population is

The p-value is a probability that measures the support (or lack of support) for the

The level of significance

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. The p-value is between

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

It is said that more males register to vote in a national election than females. A research organization selected a random sample of 300 registered voters and reported that 165 of the registered voters were male. a.Formulate the hypotheses for this problem. b.Compute the standard error of . c.Compute the test statistic. d.Using the p-value approach, can you conclude that more males registered to vote than females? Let $\alpha$ = .05.

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t =

The probability of making a Type I error is denoted by

The probability of making a Type II error is denoted by

Exhibit 9-2 n = 64 = 50 s = 16 H₀: $\mu$ 54 H_a: $\mu$ < 54 -Refer to Exhibit 9-2. If the test is done at 95% confidence, the null hypothesis should

Given the following information, the test statistic is n = 49 = 50 S = 7 H_o: $\mu$ > 52 H_a: $\mu$ < 52 The test statistic for the above information 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. At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A

Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon. a.Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate. b.Compute the test statistic. c.What is the p-value associated with the sample results and what is your conclusion? Let $\alpha$ = .05.

Exhibit 9-2 n = 64 = 50 s = 16 H₀: $\mu$ 54 H_a: $\mu$ < 54 -Refer to Exhibit 9-2. The test statistic equals

In the hypothesis testing procedure, $\alpha$ is

Confirmed cases of West Nile virus in birds for a sample of six counties in the state of Georgia are shown below. We are interested in testing the following hypotheses regarding these data: H₀: $\mu$ 3 H_a: $\mu$ > 3 a.Compute the mean and the standard deviation of the sample. b.Compute the standard error of the mean. c.Determine the test statistic. d.Determine the p-value and at 95% confidence, test the hypotheses.

From a population of cans of coffee marked "12 ounces," a sample of 50 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces. a.Formulate the hypotheses to test to see if the mean of the population is at least 12 ounces. b.Compute the test statistic. c.Using the p-value approach, what is your conclusion? Let $\alpha$ = .05.

The average starting salary of students who graduated from colleges of Business in 2009 was $48,400. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $8,000. We want to determine whether or not there has been a significant increase in the starting salaries. 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 for this test. d.What do you conclude? e.Compute the p-value.

Which of the following does not need to be known in order to compute the p-value?