Chapter 9

For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = 2.09. 0.0172 0.0183 0.0611 0.0415

0.0183

For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = -1.55. 0.0172 0.0901 0.1512 0.0606

0.0606

For the following z-test statistic, compute the p-value assuming that the hypothesis test is a one-tailed test: z = 1.34. 0.0124 0.0815 0.0606 0.0901

0.0901

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis? 16.2 ounces 15.8 ounces 16.049 ounces 16.041 ounces

16.041 ounces

For the following hypothesis test: H0: u <= 45 Ha: u > 45 alpha = 0.02 With n = 80, σ = 9, and xbar = 47.1, state the calculated value of the test statistic z. 3.151 -3.121 -2.141 2.087

2.087

If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: H0 : μ = 100 HA : μ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail. True False

False

In a two-tailed hypothesis test the area in each tail of the rejection region is equal to α. True False

False

The Adams Shoe Company believes that the mean size for men's shoes is now more than 10 inches. To test this, it has selected a random sample of n = 100 men. Assuming that the test is to be conducted using a .05 level of significance, a p-value of .07 would lead the company to conclude that its belief is correct. True False

False

The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: H0: μ < 50 HA : μ > 50 True False

False

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. Use α = 0.05. Establish the appropriate null and alternative hypotheses to be tested for boxes that are supposed to have an average of 24 ounces. H0 : μ = 22 ounces Ha : μ ≠ 22 ounces H0 : μ = 16 ounces Ha : μ ≠ 16 ounces H0 : μ = 32 ounces Ha : μ ≠ 32 ounces H0 : μ = 24 ounces Ha : μ ≠ 24 ounces

H0 : μ = 24 ounces Ha : μ ≠ 24 ounces

According to CNN business partner Careerbuilder.com, the average starting salary for accounting graduates in 2008 was at least $47,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. State the appropriate null and alternative hypotheses. H0 : μ ≤ $47,413 HA : μ > $47,413 H0 : μ < $47,413 HA : μ ≥ $47,413 H0 : μ > $47,413 HA : μ ≤ $47,413 H0 : μ ≥ $47,413 HA : μ < $47,413

H0 : μ ≥ $47,413 HA : μ < $47,413

Waiters at Finegold's Restaurant and Lounge earn most of their income from tips. Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses. The manager has based the "tip-out" rate on the assumption that the mean tip is at least 15% of the customer bill. To make sure that this is the correct assumption, he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. State the appropriate null and alternative hypotheses. H0 : μ ≥ 9 Ha : μ < 9 H0 : μ ≤ 9 Ha : μ > 9 H0 : μ ≥ 15 Ha : μ < 15 H0 : μ ≤ 15 Ha : μ > 15

H0 : μ ≥ 15 Ha : μ < 15

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats, the sample mean of 16 boxes was 24.32 ounces, with a standard deviation of 0.70 ounce. Assist the production control manager in determining if the machine is achieving its targeted average at alpha = 0.05. Process is not running okay therefore reject H0 Process is running okay, reject the Ho: Process is running okay, do not reject H0 Process is not running okay, reject the Ho

Process is running okay, do not reject H0

A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course. To test this, a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test. These students will take the company's course and then retake the SAT test. Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05, find the critical value in terms of improvement in SAT points. Reject the null if SAT improvement is > 95 points. Reject the null if SAT improvement is > 94.935 points. Reject the null if SAT improvement is > 95.88 points. Reject the null if SAT improvement is 85.065 points.

Reject the null if SAT improvement is > 94.935 points

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based on this sample information, he decides if the desired standard is not being met. He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise. On one occasion where a sample of 40 customers was selected, the average number of days was 6.65, with a sample standard deviation of 1.5 days. Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question. Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.4421 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.2346 < 2.5113, reject H0 and conclude that the mail-order business is not achieving its goal. Since 2.2216 < 2.4511, reject H0 and conclude that the mail-order business is not achieving its goal

Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.

A local medical center has advertised that the mean wait for services will be less than 15 minutes. Given this claim, the hypothesis test for the population mean should be a one-tailed test with the rejection region in the lower (left-hand) tail of the sampling distribution. True False

True

In conducting a hypothesis test where the conclusion is to reject the null hypothesis, then either a correct decision has been made or else a Type I error. True False

True

In hypothesis testing, the null hypothesis should contain the equality sign. True False

True

The null and alternate hypotheses must be opposites of each other. True False

True

When the decision maker has control over the null and alternative hypotheses, the alternative hypotheses should be the "research" hypothesis. True False

True

When someone is on trial for suspicion of committing a crime, the hypotheses are: H0 : innocent HA : guilty Which of the following is correct? Type II error is convicting an innocent person. Type I error is convicting an innocent person. Type I error is acquitting a guilty person. Type II error is acquitting an innocent person.

Type I error is convicting an innocent person.

The cost of a college education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. To test this at a significance level of 0.05, a random sample of n = 20 students was selected and the following values were observed: 26 15 10 40 10 20 30 36 40 0 5 10 20 32 16 12 40 36 10 0 Based on these sample data, the critical value expressed in hours: is approximately equal to 25.0 hours. is approximately equal to 25.26 hours. is approximately 22 hours. cannot be determined without knowing the population standard deviation.

is approximately equal to 25.26 hours.

The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes. A random sample of 100 customers was taken. The average length of calling time in the sample was 3.1 minutes with a standard deviation of 0.5 minutes. At a 0.05 level of significance, it can be concluded that the mean of the population is: significantly less than 3. significantly greater than 3. not significantly greater than 3. not significantly different from 3.10.

significantly greater than 3.

If the p value is less than α in a two-tailed test, a one-tailed test should be used. the null hypothesis should not be rejected. the null hypothesis should be rejected. More information is needed to reach a conclusion about the null hypothesis.

the null hypothesis should be rejected.

A hypothesis test is to be conducted using an alpha = .05 level. This means: there is a maximum 5 percent chance that a true null hypothesis will be rejected. there is a 5 percent chance that the null hypothesis is true. there is a 5 percent chance that a Type II error has been committed. there is a 5 percent chance that the alternative hypothesis is true.

there is a maximum 5 percent chance that a true null hypothesis will be rejected.