At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation $\sigma$= 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

State the hypotheses.

The chamber of commerce of a Florida Gulf Coast community advertises that area residential property is available at a mean cost of $125,000 or less per lot. Suppose a sample of 32 properties provided a sample mean of$130,000 per lot and a sample standard deviation of $12,500. Use a .05 level of significance to test the validity of the advertising claim.

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.

Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.

The file Eagle contains the sample data. Develop a point estimate of the population proportion.

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than $10 \%$ of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.

Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.

The file Eagle contains the sample data. Develop a point estimate of the population proportion.

Use $\alpha=.05$ to conduct your hypothesis test. Should Eagle go national with the promotion?

At Western University the historical mean of scholarship examination scores for freshman applications is 900 . A historical population standard deviation $\sigma=180$ is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

State the hypotheses.

What is the $95 \%$ confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean of $\bar{x}=935$ ?

Use the confidence interval to conduct a hypothesis test. Using $\alpha=.05$, what is your conclusion?

What is the $p$-value?

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \geq 45 } \\ { H _ { \mathrm { a } } : \mu < 45 } \end{array}$$

A sample of 36 is used. Identify the $p$ -value and state your conclusion for each of the fol- lowing sample results. Use $\alpha = .01 .$

$\overline { x } = 44$ and $s = 5.2$

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.

Develop the appropriate null and alternative hypotheses.

According to the IRS, taxpayers calling the IRS in $2017$ waited $13$ minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of $50$ callers who placed their calls to the IRS in the first $30$ minutes that the line is open during the day have a mean waiting time of $11$ minutes before an IRS telephone assister answers. Based on data from past years, you decide that it is reasonable to assume that the standard deviation of waiting times is $8$ minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first $30$ minutes the IRS help line is open each day is significantly less that the overall mean waiting time of $13$ minutes? Use $\alpha$ $= .05$

Ten years ago, $53 \%$ of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now $46 \%$.

b. Assume the Investment Company Institute, sampled 300 American families to estimate that the percent owning stocks or stock funds was $46 \%$ in 2012. What is the $p$-value for your hypothesis test?

A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.

Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 12 } \\ { H _ { \mathrm { a } } : \mu > 12 } \end{array}$$

A sample of 25 provided a sample mean $\overline { x } = 14$ and a sample standard deviation $s = 4.32$.

Compute the value of the test statistic.

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.

Use $\alpha= .05$ to conduct your hypothesis test. Should Eagle go national with the promotion?