Question

1. Objectives:

1) Select a simple random sample by random number table or Excel.

2) Know the sampling distribution of and, and calculate the probabilities by excel.

Q1: The director of personnel for Electronics Associates, Inc (EAI), has been assigned the task of developing a profile of the company’s 250 managers. The characteristics to be identified include the mean annual salary for the managers and the proportion of managers have completed the company’s management training program. Using the 2500 managers as the population for this study. (See data in a file named EAI).

Select a simple random sample of 30 managers from the 2500 EAI managers.

Q2: Business Weej conducted a survey of graduates from 30 top MBA programs (Business-Week, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates, it is $25,000.

a. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000?

b. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000?

c. In which of the preceding two cases, part (a) and part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Comment on the results.

Q3: The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion p=0.76, and a sample of 400 consumers is selected from the population.

a. Show the sampling distribution of the sample proportion, where is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

b. What is the probability that the sample proportion will be within +- 0.03 of the population proportion?

c. Answer part (b) for a sample of 750 consumers.

Answer 1

Q2) Given that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates, it is $25,000.

a) The salary of males 10 years after graduation is normally distributed with

The sample mean has distribution . Here

The probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000

b) As in part (a),  the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 is

c) Females have a higher probability of obtaining a sample estimate within $10,000 of the population mean. This is because the sample size being the same, the salaries of Females have lesser standard deviation

We are required to solve only one question. Please post the remaining questions as another post.