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?

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%.

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.

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.

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.

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 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.

(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%.

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.

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.

Some people are allergic to wheat or wheat gluten. But people with this problem can still get plenty of healthful grains in their diets if they plan carefully. For example, some bakeries substitute the wheat in bread with a grain called spelt. Corn flour is also a nourishing alternative to wheat fl our. Based on the paragraph, which of the following best completes the following sentence? People who are allergic to wheat ____. a. cannot eat corn tortillas b. can substitute other grains for wheat c. can eat wheat if they pair it with another grain d. cannot tolerate bread

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 ?