QUESTION 4

State whether each of the following are TRUE or FALSE, and explain your reasoning for the answer:

1. The binomial distribution is defined by its mean and standard deviation.

2. As the sample size increases, the standard error of the mean decreases.

3. If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 10 observations.

(b)       Suppose the following trend line and seasonal indices were obtained from four (4) years of sales data (in $ million) for a multinational grocery chain from 2012 to 2015.

Trend line:        y_t = 112 + 2.6t

Seasonal Effect:

1. Interpret fully the seasonal indices for the first and second quarters.

   (1 mark)

2. Forecast the sales value in the fourth quarter for the next year (2016).

(1 mark)

            You have decided to open a restaurant in Huntington. The following table gives the payoffs based on two states of nature, favorable and unfavorable demand. You     believe that the probability of a favorable market is 0.8. You can open any one of        three different sizes of restaurant.     

            You have decided to do some marketing research (using the skills that you learned). If the marketing research is positive (probability = .7), then the probability of favorable demand goes to .95. If the marketing research is negative (shows weak demand) (probability of .3), then the probability of favorable demand goes to .40.

1. Using all of the information, what should you do? Provide calculations.

2. What is the expected value of perfect information?

3. What is the expected value of sample information?

Exercise 9-7

Sarasota Company follows the practice of pricing its inventory at the lower-of-cost-or-market, on an individual-item basis.

From the information above, determine the amount of Sarasota Company inventory.

Your firm specializes in the construction of short track speed skating ice rinks. The popularity of this sport at the Winter Olympics has resulted in lots of new business for your firm. To meet this demand, you've decided to buy or lease a new Terex tower crane for use over the next four years. You have two choices:
1)Buy the crane from Terex for $600,000 and sell it back to them in 48 months for $240,000.
2)Lease the crane from Terex for $11,000 per month for 48 months. If you choose to lease the crane, they will make the first and last payments on your behalf (so that you only have to make payments in months 2 through 47).
Your opportunity cost of capital is 0.8% per month. Should you lease or buy the new crane?

SHOW YOUR WORK, DO NOT USE EXCEl

An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed withσ = 70 psi. A random sample of 12 specimens has a mean ten-sile strength of x = 3450 psi.

(a) Test the hypothesis that mean strength is 3500 psi. Use α = 0.05.

(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?

(c) What is the β-error for the test in part (a) if the true mean is 3470?

(d) Suppose that you wanted to reject the null hypothesis with probability at least 0.8 if mean strength μ = 3470. What sample size should be used?

(e) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.

Suppose that Apex HealthServices has four difference projects.These projects are listed below, along with the amount of capital invested and estimated corporate and market betas: Project Amount Invested Corporate beta Market Betas walk-in-clinic 500,000 1.5 1.1 MRI facility 2,000,000 1.2 1.5 Clinical laboratory 1,500,000 0.9 0.8 X-ray laboratory 1,000,000 0.5 1.0 5,000,000 (a)why do the corporate and market betas differ for the same project? (b)what is the overall corporate beta of Apex HealthServices? Is the calculated beta consistent with corporate risk theroy? (c)what is the overall market beta of Apex Health services? (d) How does the riskiness of Apex's stock compare with the riskiness of an average stock? (e) would stock investors required rate of return on Apex that is greater than, less than,or the same as the return on an average-risk stock?

1a. Given: mean difference between men and women = 2.2; standard error of mean difference = 0.8; n men = 61, n women = 61.

Test the following null hypothesis at a=.05

Ho: u men = u women

Ha: u men > u women

You need to compute the t statistic, look up t critical value and make decision including likelihood of appropriate error. You don't have to compute the standard error of mean difference because it's given.

1b. Compute the appropriate confidence interval for the two-sample t-test of the previous question. Make sure you look at the alternative hypothesis before computing this interval.

Please upload into a Microsoft Word file and show work for answers

For 1b. please show work by doing step by step. line margins

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

(a) Use the Normal approximation to find the probability that Jodi scores 74% or lower on a 100-question test. (Round your answer to four decimal places.)

(b) If the test contains 250 questions, what is the probability that Jodi will score 74% or lower? (Use the normal approximation. Round your answer to four decimal places.)

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?