A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis?

$$H_0:μ≤10; H_1:μ>10$$

(a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding

$$H_0?$$

(e) What is the p-value? Interpret it. A recent national survey found that high school students watched an average of 6.8 DVDs per month with a population standard deviation of 0.5 hours. The distribution of times follows the normal distribution. A random sample of 36 college students revealed that the mean number of DVDs watched last month was 6.2. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

A random sample of 10 observations from population A has a sample mean of 152.30 and a sample standard deviation of 1.83. A random sample of 8 observations from population B has a sample standard deviation of 1.94. If the $p$-value for the one-sided hypothesis test with an alternative hypothesis $H_A : \mu_A > \mu_B$ is less than $1\%$, what can you say about the sample mean of the observations from population B?

A national grocer’s magazine reports the typical shopper spends eight minutes in line waiting to check out. A sample of 24 shoppers at the local Farmer Jack’s showed a mean of 7.5 minutes with a standard deviation of 3.2 minutes. Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the .05 significance level.

Answer the questions: (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding

$$H_0?$$

A sample of 36 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level.

$$H_0:μ≤20; H_1:μ>20$$

The null and alternate hypotheses are:

$$H_0:μ_1=μ_2; H_1:μ_1≠μ_2$$

A random sample of 10 observations from one population revealed a sample mean of 23 and a sample deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means?

Answer the questions: (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding

$$H_0?$$

A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the .02 significance level.

$$H_0:μ≤10; H_1:μ>10$$

The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 2.1 calls. Using the .05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40?

A random sample of n observations is selected from a normal population to test the null hypothesis that

$$\mu = 10$$

Specify the rejection region for each of the following combinations of

$$H _ { a } , \alpha , \text { and } n$$

$$H _ { a } : \mu \neq 10 ; \alpha = .05 ; n = 14$$

The mean income per person in the united states is $\$60 000$ and the distribution of incomes follows a normal distribution. A random sample of $10$ residents of Wilmington, Delaware had a mean of $\$70 000$ with a standard deviation of $\$10 000$. At the $0.05$ level of significance is that enough evidence to conclude that residents of Wilmington, Delaware have more income than the national average?

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. a. What is the point estimate of the population mean? b. Develop a 99 percent confidence interval for the population mean. c. Interpret the meaning of part (b).

A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?

Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a long history, management knows that the distribution of bag weights is normally distributed with a population standard deviation of 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Following are the weights of 10 bags from today's production.

$$\begin{array}{llllllllll} 45.6 & 47.7 & 47.6 & 46.3 & 46.2 & 47.4 & 49.2 & 55.8 & 47.5 & 48.5 \end{array}$$

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in: a. More than 20 minutes? b. For 20 minutes or less? c. Between 10 and 12 minutes?