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 ?

A random sample of 50 students was asked what salary the college should be prepared to pay to attract the right individual to coach the football team. An independent random sample of 50 faculty members was asked the same question. The 100 salary figures were then pooled and ranked in order (with rank 1 assigned to the lowest salary). The sum of the ranks for faculty members was 2,024. Test the null hypothesis that there is no difference between the central locations of the distributions of salary proposals of students and faculty members against the alternative that in the aggregate students would propose a higher salary to attract a football coach.

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

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.

Javier is an IE at Lobos Manufacturing. He has been studying process line G to determine if an automated system would be preferred to the existing labor intensive system. If Lobos wants to earn at least 20% and uses a 15-year planning horizon, which alternative is preferred.

In our discussion of TCP congestion control in earlier Section, we implicitly assumed that the TCP sender always had data to send. Consider now the case that the TCP sender sends a large amount of data and then goes idle (since it has no more data to send) at $t_1$. TCP remains idle for a relatively long period of time and then wants to send more data at $t_2$. What are the advantages and disadvantages of having TCP use the cwnd and ssthresh values from $t_1$ when starting to send data at $t_2$ ? What alternative would you recommend? Why?

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?

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

(a) state the null and alternative hypotheses and identify which represents the claim, (b) describe type I and type II errors for a hypothesis test of the claim, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed, (d) explain how you should interpret a decision that rejects the null hypothesis, and (e) explain how you should interpret a decision that fails to reject the null hypothesis. A polling organization reports that the proportion of U.S. adults who have volunteered their time or donated money to help clean up the environment is 65%.

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.

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.

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

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

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.

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.

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 $\beta_1$.