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 $\alpha$ $= .05$

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.

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.

Annual expenditure for prescription drugs was $838 per person in the Northeast of the country (Hospital Care Cost Institute website, November 7, 2012). A sample of 60 individuals in the Midwest showed a per person annual expenditure for prescription drugs of$745. Use a population standard deviation of $300 to answer the following questions.

a. Formulate hypotheses for a test to determine whether the sample data support the conclusion that the population annual expenditure for prescription drugs per person is lower in the Midwest than in the Northeast.

b. What is the value of the test statistic?

c. What is the p-value?

d. At$\alpha=.01$, what is your conclusion?

TextRequest reports that adults $18-24$ years old send and receive $128$ texts every day. Suppose we take a sample of $25-34$ year olds to see if their mean number of daily texts differs from the mean for $18-24$ year olds reported by TextRequest.
a. State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for $25-34$ year olds differs from the population daily mean number of texts for $18-24$ year olds.
b. Suppose a sample of thirty $25-34$ year olds showed a sample mean of $118.6$ texts per day. Assume a population standard deviation of 33.17 texts per day and compute the $p$-value.
c. With $\alpha=.05$ as the level of significance, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.\

TextRequest reports that adults 18–24 years old send and receive 128 texts every day. Suppose we take a sample of 25–34 year olds to see if their mean number of daily texts differs from the mean for 18–24 year olds reported by TextRequest.

State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

According to the the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Data for the sale of 40 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017.

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.

What is the p-value?

TextRequest reports that adults 18–24 years old send and receive 128 texts every day. Suppose we take a sample of 25–34 year olds to see if their mean number of daily texts differs from the mean for 18–24 year olds reported by TextRequest.

Suppose a sample of thirty 25–34 year olds showed a sample mean of 118.6 texts per day. Assume a population standard deviation of 33.17 texts per day and compute the p-value

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.

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.

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

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.

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 50 } \\ { H _ { \mathrm { a } } : \mu > 50 } \end{array}$$

A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use $\alpha = .05$.

$$\overline { x } = 52.5$$