Exam 9: Hypothesis Tests

A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters. a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let α = .05.

Choo Choo Paper Company makes various types of paper products. One of their products is a 30 mils thick paper. In order to ensure that the thickness of the paper meets the 30 mils specification, random cuts of paper are selected and the thickness of each cut is measured. A sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. a. Compute the standard error of the mean. b. b. At 95% confidence using the critical value approach, test to see if the mean thickness is significantly more than 30 mils. c. Show that the p-value approach results in the same conclusion as that of part

In a one-tailed hypothesis test lower tail) the test statistic is determined to be -2. The p-value for this test is

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 α = .05.

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

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 two-tailed test, a sample of 20 at 80% confidence, t =

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 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.

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

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

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

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

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50 with a standard deviation of $16. a. Formulate the hypotheses to determine whether or not the average room price is significantly different from $112. b. Compute the test statistic. c. At 95% confidence using the p-value approach, test the hypotheses. Let α = 0.1.

Exhibit 9-1 =36 =24.6 =12 :\mu\leq20 :\mu>20 -Refer to Exhibit 9-1. The test statistic is

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

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

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

Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 400 employees, 180 were female. a. Give the null and the alternative hypotheses. b. b. At 95% confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females. c. Show that the p-value approach results in the same conclusion as that of Part