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.

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 marketing research firm wishes to compare the prices charged by two supermarket chains-Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at $10$ of each chain's stores. The stores for each chain are randomly selected, and all purchases are made during a single week.

The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

$$\begin{array}{lllll}\text { Miller's } & & & & \\ \$ 119.25 & \$ 121.32 & \$ 122.34 & \$ 120.14 & \$ 122.19 \\ \$ 123.71 & \$ 121.72 & \$ 122.42 & \$ 123.63 & \$ 122.44\end{array}$$

$$\begin{array}{lllll}\text { Albert's } & & & & \\\$ 111.99 & \$ 114.88 & \$ 115.11 & \$ 117.02 & \$ 116.89 \\ \$ 116.62 & \$ 115.38 & \$ 114.40 & \$ 113.91 & \$ 111.87\end{array}$$

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed.

Set up the null and alternative hypotheses needed to attempt to establish that the mean weekly expense for the shopping plan at Miller's exceeds the mean weekly expense at Albert's by more than $\$ 5$. Test the hypotheses at the $.10$, $.05$, $.01$, and $.001$ levels of significance. How much evidence is there that the mean weekly expense at Miller's exceeds that at Albert's by more than $\$ 5$?

A marketing research firm wishes to compare the prices charged by two supermarket chains-Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at $10$ of each chain's stores. The stores for each chain are randomly selected, and all purchases are made during a single week.

The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

$$\begin{array}{lllll}\text { Miller's } & & & & \\ \$ 119.25 & \$ 121.32 & \$ 122.34 & \$ 120.14 & \$ 122.19 \\ \$ 123.71 & \$ 121.72 & \$ 122.42 & \$ 123.63 & \$ 122.44\end{array}$$

$$\begin{array}{lllll}\text { Albert's } & & & & \\\$ 111.99 & \$ 114.88 & \$ 115.11 & \$ 117.02 & \$ 116.89 \\ \$ 116.62 & \$ 115.38 & \$ 114.40 & \$ 113.91 & \$ 111.87\end{array}$$

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed.

Figure $10.5$ gives a $95$ percent confidence interval for $\mu_M-\mu_A$. Use this confidence interval to describe the size of the difference between the mean weekly expenses at Miller's and Albert's. Do you think that these means differ in a practically important way?

Figure $10.5$ Minitab Output of Testing the Equality of Mean Weekly Expenses at Miller’s and Albert’s Supermarket Chains Two-sample $\mathrm{T}$ for Millers vs Alberts

$$\begin{array}{lrrrr} & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } \\ \text { Millers } & 10 & 121.92 & 1.40 & 0.44 \\ \text { Alberts } & 10 & 114.81 & 1.84 & 0.58\end{array}$$

Difference $=\mathbf{m u}$ (Millers) $-\mathbf{m u}$ (Alberts)$\quad$ Estimate for difference: $7.10900$ $95 \%$ CI for difference: $(5.57350,8.64450)$ T-Test of diff $=0($ vs not $=):$ T-Value $=9.73 \quad \mathrm{P}$-Value $=0.000 \quad \mathrm{DF}=18$ Both use Pooled StDev $=1.6343$

A marketing research firm wishes to compare the prices charged by two supermarket chains-Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at $10$ of each chain's stores. The stores for each chain are randomly selected, and all purchases are made during a single week.

The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

$$\begin{array}{lllll}\text { Miller's } & & & & \\ \$ 119.25 & \$ 121.32 & \$ 122.34 & \$ 120.14 & \$ 122.19 \\ \$ 123.71 & \$ 121.72 & \$ 122.42 & \$ 123.63 & \$ 122.44\end{array}$$

$$\begin{array}{lllll}\text { Albert's } & & & & \\\$ 111.99 & \$ 114.88 & \$ 115.11 & \$ 117.02 & \$ 116.89 \\ \$ 116.62 & \$ 115.38 & \$ 114.40 & \$ 113.91 & \$ 111.87\end{array}$$

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed.

Figure $10.5$ gives the $p$-value for testing $H_0: \mu_M-\mu_A=$ 0 versus $H_a: \mu_M-\mu_A \neq 0$. Use the $p$-value to test $H_0$ versus $H_a$ by setting $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ?

Figure $10.5$ Minitab Output of Testing the Equality of Mean Weekly Expenses at Miller’s and Albert’s Supermarket Chains Two-sample $\mathrm{T}$ for Millers vs Alberts

$$\begin{array}{lrrrr} & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } \\ \text { Millers } & 10 & 121.92 & 1.40 & 0.44 \\ \text { Alberts } & 10 & 114.81 & 1.84 & 0.58\end{array}$$

Difference $=\mathbf{m u}$ (Millers) $-\mathbf{m u}$ (Alberts)$\quad$ Estimate for difference: $7.10900$ $95 \%$ CI for difference: $(5.57350,8.64450)$ T-Test of diff $=0($ vs not $=):$ T-Value $=9.73 \quad \mathrm{P}$-Value $=0.000 \quad \mathrm{DF}=18$ Both use Pooled StDev $=1.6343$

A marketing research firm wishes to compare the prices charged by two supermarket chains-Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at $10$ of each chain's stores. The stores for each chain are randomly selected, and all purchases are made during a single week.

The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

$$\begin{array}{lllll}\text { Miller's } & & & & \\ \$ 119.25 & \$ 121.32 & \$ 122.34 & \$ 120.14 & \$ 122.19 \\ \$ 123.71 & \$ 121.72 & \$ 122.42 & \$ 123.63 & \$ 122.44\end{array}$$

$$\begin{array}{lllll}\text { Albert's } & & & & \\\$ 111.99 & \$ 114.88 & \$ 115.11 & \$ 117.02 & \$ 116.89 \\ \$ 116.62 & \$ 115.38 & \$ 114.40 & \$ 113.91 & \$ 111.87\end{array}$$

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed.

Using the $t$ statistic given on the output and critical values, test $H_0$ versus $H_a$ by setting $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ?

A marketing research firm wishes to compare the prices charged by two supermarket chains-Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at $10$ of each chain's stores. The stores for each chain are randomly selected, and all purchases are made during a single week.

The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

$$\begin{array}{lllll}\text { Miller's } & & & & \\ \$ 119.25 & \$ 121.32 & \$ 122.34 & \$ 120.14 & \$ 122.19 \\ \$ 123.71 & \$ 121.72 & \$ 122.42 & \$ 123.63 & \$ 122.44\end{array}$$

$$\begin{array}{lllll}\text { Albert's } & & & & \\\$ 111.99 & \$ 114.88 & \$ 115.11 & \$ 117.02 & \$ 116.89 \\ \$ 116.62 & \$ 115.38 & \$ 114.40 & \$ 113.91 & \$ 111.87\end{array}$$

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed.

Letting $\mu_M$ be the mean weekly expense for the shopping plan at Miller's, and letting $\mu_A$ be the mean weekly expense for the shopping plan at Albert's, gives the Minitab output of the test of $H_0: \mu_M-\mu_A=0$ (that is, there is no difference between $\mu_M$ and $\mu_A$ ) versus $H_a: \mu_M-\mu_A \neq 0$ (that is, $\mu_M$ and $\mu_A$ differ). Note that Minitab has employed the equal variances procedure. Use the sample data to show that $\bar{x}_M=121.92, s_M=1.40, \bar{x}_A=114.81$, $s_A=1.84$, and $t=9.73$.

For each of the formulas described below, list all of the assumptions that must be satisfied in order to validly use the formula.

The confidence interval in the formula box on the given page.

Suppose that a national survey finds that $73$ percent of restaurant employees say that work stress has a negative impact on their personal lives. A random sample of $200$ employees of a large restaurant chain finds that $141$ employees say that work stress has a negative impact on their personal lives. (1) Formulate the null and alternative hypotheses needed to attempt to provide evidence that the percentage of work-stressed employees for the restaurant chain differs from the national percentage. (2) Use critical values and a $p$-value to perform the hypothesis test by setting $\alpha$ equal to $.10, .05, .01$, and $.001$.

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a marketing research proposal to study day-after recall for a brand of mouthwash. To quote the authors:

The ad agency has developed a TV ad for the introduction of the mouthwash. The objective of the ad is to create awareness of the brand. The objective of this research is to evaluate the awareness generated by the ad measured by aided-and unaided-recall scores. A minimum of $200$ respondents who claim to have watched the TV show in which the ad was aired the night before will be contacted by telephone in $20$ cities. The study will provide information on the incidence of unaided and aided recall.

Suppose a random sample of $200$ respondents shows that $46$ of the people interviewed were able to recall the commercial without any prompting (unaided recall).

Do you think the result of the ad agency’s survey has practical importance? Explain your opinion.

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a marketing research proposal to study day-after recall for a brand of mouthwash. To quote the authors:

The ad agency has developed a TV ad for the introduction of the mouthwash. The objective of the ad is to create awareness of the brand. The objective of this research is to evaluate the awareness generated by the ad measured by aided-and unaided-recall scores. A minimum of $200$ respondents who claim to have watched the TV show in which the ad was aired the night before will be contacted by telephone in $20$ cities. The study will provide information on the incidence of unaided and aided recall.

Suppose a random sample of $200$ respondents shows that $46$ of the people interviewed were able to recall the commercial without any prompting (unaided recall).

Use the previously given sample information to: $\mathbf{(1)}$ Compute the $p$-value for the hypothesis test you set up in part $a$. $\mathbf{(2)}$ Use the $p$-value to carry out the test by setting $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. $\mathbf{(3)}$ How much evidence is there that the TV commercial is successful?

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a marketing research proposal to study day-after recall for a brand of mouthwash. To quote the authors:

The ad agency has developed a TV ad for the introduction of the mouthwash. The objective of the ad is to create awareness of the brand. The objective of this research is to evaluate the awareness generated by the ad measured by aided-and unaided-recall scores. A minimum of $200$ respondents who claim to have watched the TV show in which the ad was aired the night before will be contacted by telephone in $20$ cities. The study will provide information on the incidence of unaided and aided recall.

Suppose a random sample of $200$ respondents shows that $46$ of the people interviewed were able to recall the commercial without any prompting (unaided recall).

In order for the ad to be considered successful, the percentage of unaided recall must be above the category norm for a TV commercial for the product class. If this norm is $18$ percent, set up the null and alternative hypotheses needed to attempt to provide evidence that the ad is successful.

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss evaluating the effectiveness of a test coupon. Samples of $500$ test coupons and $500$ control coupons were randomly delivered to shoppers. The results indicated that $35$ of the $500$ control coupons were redeemed, while $50$ of the $500$ test coupons were redeemed.

In order to consider the test coupon for use, the marketing research organization required that the proportion of all shoppers who would redeem the test coupon be statistically shown to be greater than the proportion of all shoppers who would redeem the control coupon. Assuming that the two samples of shoppers are independent, carry out a hypothesis test at the $.01$ level of significance that will show whether this requirement is met by the test coupon. Explain your conclusion.

Recall that a conflict of interest scenario was presented to a sample of $205$ marketing researchers and that $111$ of these researchers disapproved of the actions taken.

Note that in parts $b$ and $c$ the sample proportion $\hat{p}$ is (essentially) the same. Explain why the results of the hypothesis tests in parts $b$ and $c$ differ.