Exam 9: Hypothesis Tests

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 σ) 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 α = .05. c. Using the p-value approach, test the hypotheses at the 5% level of significance.

A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.8 with a standard deviation of 3. 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 hypothesis at the 5% level of significance. d. Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.

For a two-tailed test at 98.4% confidence, Z =

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. -Refer to Exhibit 9-6. At 95% confidence, it can be concluded that the mean age is

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

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 σ) is $0.14. -Refer to Exhibit 9-8. The p-value for this problem is

For a one-tailed test lower tail) with 22 degrees of freedom at 95% confidence, the value of t =

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

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

The probability of making a Type I error is denoted by

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

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

For a two-tailed test at 86.12% confidence, Z =

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

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. -Refer to Exhibit 9-6. The p-value is between

Confirmed cases of West Nile virus in birds for a sample of six counties in the state of Georgia are shown below. County Cases Catoosa 6 Chattooga 3 Dade 3 Gordon 5 Murray 3 Walker 4 We are interested in testing the following hypotheses regarding these data: Ho: μ ≤ 3 Ha: μ > 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.

What type of error occurs if you fail to reject H0 when, in fact, it is not true?

The probability of making a Type II error is denoted by

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 p-value is

A group of young businesswomen wish to open a high fashion boutique in a vacant store but only if the average income of households in the area is at least $25,000. A random sample of 9 households showed the following results. \ 28,000 \ 24,000 \ 26,000 \ 25,000 \ 23,000 \ 27,000 \ 26,000 \ 22,000 \ 24,000 Assume the population of incomes is normally distributed. a. Compute the sample mean and the standard deviation. b. State the hypotheses for this problem. c. Compute the test statistic. d. At 95% confidence using the p-value approach, what is your conclusion?