In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced by a particular species of mussel found ff the coast of New Zealand. To test this claim, the mussel extract is to be given to a group of 7 osteoarthritic patients. If 3 or more of the patients receive relief, we shall not reject the null hypothesis that p =0 .4; otherwise, we conclude that p < 0.4. (a) Evaluate $\alpha$ assuming that p = 0.4. (b) Evaluate $\beta$ for the alternative p = 0.3.

A bank conducts a survey in which it randomly samples 400 of its customers. The survey asks the customers which way they use the bank the most:

(1) interacting with a teller at the bank,

(2) using ATMs, or

(3) using the bank's online banking service.

It also asks their level of satisfaction with the service they most often use (on a scale of 0 to 10 with 0 = very poor and 10 = excellent). Does mean satisfaction differ according to how they most use the bank?

Identifying notation, state the null and alternative hypotheses for conducting an ANOVA with data from the survey.

Consider the following alternatives:

$$\begin{matrix} \text{ } & \text{A} & \text{B} & \text{C}\\ \text{Initial cost} & \text{\$10,000} & \text{\$15,000} & \text{\$20,000}\\ \text{Uniform annual benefit} & \text{1000} & \text{1762} & \text{5548}\\ \text{Useful life (years)} & \text{Infinite} & \text{20} & \text{5}\\ \end{matrix}$$

Alternatives B and C are replaced at the end of their useful lives with identical replacements. Use an infinite analysis period. (a) Construct a choice table for interest rates from 0% to 100%. (b) At an 8% interest rate, which alternative is better?

LoTech Welding can purchase a machine for $175,000 and depreciate it as 5-year MACRS property. Annual maintenance would be$9800, and its salvage value after 8 years is $15,000. The machine can also be leased for$35,000 per year on an “all costs” inclusive lease (maintenance costs included). Lease payments are due at the beginning of each year, and they are tax deductible. The firm’s combined tax rate for state and federal income taxes is 40%. If the firm’s after-tax interest rate is 9%, which alternative has the lower EAC and by how much

Fly Co. is considering the following alternative financing plans:

$$\begin{array}{lrr} & \textbf { Plan 1 } & \textbf { Plan 2 } \\ \hline \text { Issue } 12 \% \text { bonds (at face value) } & \$ 10,000,000 & \$ 5,000,000 \\ \text { Issue preferred } \$ 1.75 \text { stock, } \$ 20 \text { par } & - & 8,000,000 \\ \text { Issue common stock, } \$ 20 \text { par } & 10,000,000 & 7,000,000 \end{array}$$

Income tax is estimated at 40% of income. Determine the earnings per share of common stock, assuming income before bond interest and income tax is $2,000,000.

The following statement appeared on a box of Tide laundry detergent: “Individual packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day’s production of Tide will average slightly above the marked weight.” a. Explain in statistical terms what the statement means. b. Describe in words a hypothesis test for checking the statement. c. Suppose that the marked weight is 76 ounces. State in words the null and alternative hypotheses for the hypothesis test. Then express those hypotheses in statistical terminology.

A chocolatier claims that his candy averages at least 81 pieces per bag. Conrad randomly selects bags of the candies and counts the pieces. Assume that $\sigma=1.2.$

$$\text{Number of Pieces} \\ \begin{array}{|l|l|l|l|l|l|l|l|l|} \hline 81 & 80 & 82 & 82 & 83 & 82 & 84 & 81 & 81 \\ \hline 80 & 83 & 83 & 82 & 81 & 80 & 84 & 81 & 81 \\ \hline \end{array}$$

Write the null and alternative hypotheses, and state which hypothesis represents the claim.

Brower Co. is considering the following alternative financing plans:

$$\begin{array}{lcc} & \textbf { Plan 1 } & \textbf { Plan 2 } \\ \hline \text { Issue } 10 \% \text { bonds (at face value) } & \$ 4,000,000 & \$ 2,500,000 \\ \text { Issue preferred } \$ 2.50 \text { stock, } \$ 25 \text { par } & - & 3,000,000 \\ \text { Issue common stock, } \$ 10 \text { par } & 4,000,000 & 2,500,000 \end{array}$$

Income tax is estimated at 40% of income. Determine the earnings per share of common stock, assuming income before bond interest and income tax is $2,000,000.

Xanadu Mining is considering three mutually exclusive alternatives as shown in the table below. $MARR$ is 10 percent/year. Based on an internal rate of return analysis, which alternative should be recommended?

$$\begin{array}{|c|c|c|c|c|c|} \hline \text { EOY } & 0 & 1 & 2 & 3 & 4 \\ \hline \text { A001 } & -\$ 210 & \$ 80 & \$ 90 & \$ 100 & \$ 110 \\ \hline \text { B002 } & -\$ 110 & \$ 60 & \$ 60 & \$ 60 & \$ 70 \\ \hline \text { C003 } & -\$ 160 & \$ 80 & \$ 80 & \$ 80 & \$ 80 \\ \hline \end{array}$$

The mentioned exercise concerns a test about the mean contents of cola bottles. The hypotheses are

$$\begin{aligned} & H_0: \mu=300 \\ & H_a: \mu<300 \end{aligned}$$

The sample size is n=6, and the population is assumed to have a normal distribution with $\sigma=3$. A 5% significance test rejects $H_0$ if $z \leq-1.645$, where the test statistic z is

$$z=\frac{\bar{x}-300}{3 / \sqrt{6}}$$

Power calculations help us see how large a shortfall in the bottle contents the test can be expected to detect.

Find the power of this test against the alternative $\mu=299$.

Based on a sample of 25 observations, the population regression model

$$y_i=\beta_0+\beta_1 x_1+\varepsilon_i$$

was estimated. The least squares estimates obtained were as follows:

$$b_0=15.6 \text { and } b_1=1.3$$

The total and error sums of squares were as follows:

$$S S T=268 \text { and } \quad S S E=204$$

a. Find and interpret the coefficient of determination.

b. Test, against a two-sided alternative at the $5 \%$ significance level, the null hypothesis that the slope of the population regression line is 0 .

c. Find a $95 \%$ confidence interval for $\beta_1$.

Use the applet Hypotheses Test for a Proportion to investigate the relationships between the probabilities of Type I and Type II errors occurring at levels $.05$ and $.01$. For this exercise, use $n=100$, true $p=0.5$, and alternative not equal. Set null $p=.5$. What happens to the proportion of times the null hypothesis is rejected at the $.05$ level and at the $.01$ level as the applet is run more and more times? What type of error has occurred when the null hypothesis is rejected in this situation? Based on your results, is this type of error more likely to occur at level $.05$ or at level .01? Explain.

Alternative dividend policies Given the earnings per share over the period 20082015 shown in the following table, determine the annual dividend per share under each of the policies set forth in parts a through d.

b. Pay$0.50 per share and increase to $0.60 per share whenever earnings per share rise above$0.90 per share for two consecutive years.

Following are some summaries of the data from two separate samples drawn from normal distributions:

$$\begin{array}{ccc} \hline \text { Sample } & n & s^2 \\ \hline 1 & 11 & 3.5 \\ 2 & 16 & 9.1 \\ \hline \end{array}$$

At the $5$ significance level, you want to test the null hypothesis, which states that the two population standard deviations are equal, against the twosided alternative. (a)Calculate the test statistic in step. (b) Obtain the necessary value from Table $mathrmE$ to do the significance test. (c)What do you deduce from ?