Business Analytics

Practice 2: CH6 - Statistical Inference and Hypothesis Testing

3. A simple random sample of 5 months of sales data provided the following information:

Month: 1 2 3 4 5

Units Sold: 94 100 85 94 92

a. Develop a point estimate of the population mean number of units sold per month.

b. Develop a point estimate of the population standard deviation.

4. Morningstar publishes ratings data on 1,208 company stocks. A sample of 40 of these stocks is

contained in the file named Morningstar. Use the Morningstar data set to answer the following questions.

[Data File: Morningstar]

a. Develop a point estimate of the proportion of the stocks that receive Morningstar’s highest

rating of 5 Stars.

b. Develop a point estimate of the proportion of the Morningstar stocks that are rated Above

Average with respect to business risk.

c. Develop a point estimate of the proportion of the Morningstar stocks that are rated 2 Stars or

less.

7. The College Board reported the following mean scores for the three parts of the SAT:

Critical Reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is 𝜎 = 100.

a. For a random sample of 30 test takers, what is the sampling distribution of �̅� for scores on the Critical Reading part of the test?

b. For a random sample of 60 test takers, what is the sampling distribution of �̅� for scores on the

Mathematics part of the test?

c. For a random sample of 90 test takers, what is the sampling distribution of �̅� for scores on the

Writing part of the test?

12. The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of

age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more.

a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities

of entrepreneurs. Show the sampling distribution of �̅� where �̅� is the sample proportion of

entrepreneurs whose first startup was at 29 years of age or less.

b. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important

qualities of entrepreneurs. Show the sampling distribution of �̅� where �̅� is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.

c. Are the standard errors of the sampling distributions different in parts (a) and (b)?

Practice 2: CH6 - Statistical Inference and Hypothesis Testing

Practice 2: CH6 - Statistical Inference and Hypothesis Testing

Two Sample t-Test: Determine if there is evidence to conclude that the mean number of vacations taken

by married individuals is less than the number taken by single/divorced individuals using the data in the

Excel file Vacation Survey. Use a level of significance of 0.05. Would your conclusion change if the level

of significance is 0.01?