Suppose a sample of $11$ paired differences that has been randomly selected from a normally distributed population of paired differences yields a sample mean of $103.5$ and a sample standard deviation of $5.$

Test the null hypothesis $H_0: \mu_d \geq 110$ versus $H_a: \mu_d<110$ by setting $\alpha$ equal to $.05$ and $.01$. How much evidence is there that $\mu_d=\mu_1-\mu_2$ is less than $110$?

A large discount chain compares the performance of its credit managers in Ohio and Illinois by comparing the mean dollar amounts owed by customers with delinquent charge accounts in these two states. Here a small mean dollar amount owed is desirable because it indicates that bad credit risks are not being extended large amounts of credit. Two independent, random samples of delinquent accounts are selected from the populations of delinquent accounts in Ohio and Illinois, respectively. The first sample, which consists of $10$ randomly selected delinquent accounts in Ohio, gives a mean dollar amount of $\$ 524$ with a standard deviation of $\$ 68$. The second sample, which consists of $20$ randomly selected delinquent accounts in Illinois, gives a mean dollar amount of $\$ 473$ with a standard deviation of $\$ 22$.

Set up the null and alternative hypotheses needed to test whether there is a difference between the population mean dollar amounts owed by customers with delinquent charge accounts in Ohio and Illinois.

In the book Business Research Methods, Donald R. Cooper and C. William Emory ($1995$) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects $22$ sales trainees who are randomly divided into two experimental groups-one receives type $A$ and the other type $B$ training. The salespeople are then assigned and managed without regard to the training they have received. At the year's end, the manager reviews the performances of salespeople in these groups and finds the following results:

$$\begin{array}{lcc} & \text { A Group } & \text { B Group } \\ \text { Average Weekly Sales } & \$ 1,500 & \$ 1,300 \\ \text { Standard Deviation } & 225 & 251\end{array}$$

Use the equal variances procedure to calculate a $95$ percent confidence interval for the difference between the mean weekly sales obtained when type $A$ training is used and the mean weekly sales obtained when type $B$ training is used. Interpret this interval.

In the book Business Research Methods, Donald R. Cooper and C. William Emory ($1995$) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects $22$ sales trainees who are randomly divided into two experimental groups-one receives type $A$ and the other type $B$ training. The salespeople are then assigned and managed without regard to the training they have received. At the year's end, the manager reviews the performances of salespeople in these groups and finds the following results:

$$\begin{array}{lcc} & \text { A Group } & \text { B Group } \\ \text { Average Weekly Sales } & \$ 1,500 & \$ 1,300 \\ \text { Standard Deviation } & 225 & 251\end{array}$$

Set up the null and alternative hypotheses needed to attempt to establish that type $A$ training results in higher mean weekly sales than does type $B$ training.

On July 1, Raney Corporation purchases 500 shares of its $5 par value common stock for the treasury at a cash price of$9 per share. On September 1, it sells 300 shares of the treasury stock for cash at $11 per share. Journalize the two treasury stock transactions.

Refer to the instructions stated in the related exercise. Study the companies' balance sheets to answer the following questions:

• a. What classes of stock has each company issued?
• b. Which item carries a larger balance- the Common Stock account or Paid-In Capital in Excess of Par (also labeled Additional Paid-In Capital)?
• c. What percentage of each company's total stockholders' equity is made up of retained earnings?
• d. Do any of the companies have treasury stock? If so, how many shares and how much is the cost?

A common definition of "binge drinking" is five or more drinks at one setting for men, and four or more for women. An observational study finds that students who binge have lower average GPA than those who don't. Suggest some lurking variables that may be confounded with binge drinking. The possibility of confounding means that we can't conclude that binge drinking causes lower GPA.

Choose the best answer. Which of the following statements about the t distribution with degrees of freedom df is (are) true? I. It is symmetric. II. It has more variability than the t distribution with df + 1 degrees of freedom. III. As df increases, the t distribution approaches the standard Normal distribution. (a) I only (b) II only (c) III only (d) I and III (e) I, II, and III

For a patient in a typical hospital setting, the most important mechanism of heat loss is radiation. How does the power radiated by a patient change when the skin temperature drops from $34^{\circ} \mathrm{C}$ to $33^{\circ} \mathrm{C}$, assuming no other changes? A. It's now $99 \%$ of what it originally was. B. It's now $97 \%$ of what it originally was. C. It's now $89 \%$ of what it originally was. D. It doesn't change.

Suppose a sample of $49$ paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of $\bar{d}=5$ and a sample standard deviation of $s_d=7$

The $p$-value for testing $H_0: \mu_d \leq 3$ versus $H_a: \mu_d>3$ equals .0256. Use the $p$-value to test these hypotheses with $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. How much evidence is there that $\mu_d$ exceeds $3$? What does this say about the size of the difference between $\mu_1$ and $\mu_2$?

Suppose a sample of $49$ paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of $\bar{d}=5$ and a sample standard deviation of $s_d=7$

Test the null hypothesis $H_0: \mu_d=0$ versus the alternative hypothesis $H_a: \mu_d \neq 0$ by setting $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. How much evidence is there that $\mu_d$ differs from $0$? What does this say about how $\mu_1$ and $\mu_2$ compare?

Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of $2.57$ and a sample standard deviation of $.3$. Use critical values to test $H_0: \mu=3$ versus $H_a: \mu \neq 3$ using levels of significance $\alpha=.10, \alpha=.05, \alpha=.01$, and $\alpha=.001$.

Suppose a sample of $49$ paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of $\bar{d}=5$ and a sample standard deviation of $s_d=7$

Calculate a $95$ percent confidence interval for $\mu_d=\mu_1-\mu_2$. Can we be $95$ percent confident that the difference between $\mu_1$ and $\mu_2$ is not equal to $0$?

Recall that "very satisfied" customers give the XYZ-Box video game system a rating that is at least $42$. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of $65$ satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds $42.$

How much evidence is there that the mean composite satisfaction rating exceeds $42?$