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.

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.

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.

Frey Co. is considering the following alternative financing plans:

$$\begin{array}{lrr} & \text { Plan 1 } & \text { Plan 2 } \\ \hline \text { Issue } 5 \% \text { bonds (at face value) } & \$ 6,000,000 & \$ 2,000,000 \\ \text { Issue preferred } \$ 1 \text { stock, } \$ 20 \text { par } & - & 6,000,000 \\ \text { Issue common stock, } \$ 25 \text { par } & 6,000,000 & 4,000,000 \end{array}$$

Income tax is estimated at 40% of income.

Determine the earnings per share of common stock, assuming that income before bond interest and income tax is $800,000.

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.

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 $\mu=299$.

A pharmaceutical manufacturer is concerned that the impurity concentration in pills does not exceed 3%. It is known that from a particular production run, impurity concentrations follow a normal distribution with standard deviation 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%.

a. Test, at the 5% level, the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%.

b. Find the probability of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 3.10%.

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

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 $\beta_1$.

The consultant who advised the city on building the parking garage described predicted that the parking revenues would average $130 per day. Do the data from these two months suggest the consultant's estimate may have been incorrect? a) Write the null hypothesis. b) Decide whether you should conduct a one- or two-tail test and write an appropriate alternative hypothesis. c) Confirm that the assumptions and conditions for inference based on t-models are satisfied. d) Find the value of t and the P-value based on these data. e) State your conclusion.

Based on a sample of 30 observations, the population regression model

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

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

$$b_0=10.1 \text { and } b_1=8.4$$

The regression and error sums of squares were as follows:

$$S S R=128 \text { and } \quad S S E=286$$

a. Find and interpret the coefficient of determination.

b. Test at the $10 \%$ significance level against a twosided alternative the null hypothesis that $\beta_1$ is 0 .

c. Find

$$\sum_{i=1}^{30}\left(x_i-\bar{x}\right)^2$$

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.

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 ?