Business Statistics

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Business Statistics

Part 1

Question 1

A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126.

  1. Formulate the hypotheses that can be used to determine whether the mean of all account balances is significantly different from $1,150.
  2. Compute the test statistic.
  3. Using the p-value approach, what is your conclusion? Let α = .05.

Question 2

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.

  1. We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses.
  2. Compute the test statistic.
  3. Determine the p-value; and at 95% confidence, test the above hypotheses.

Question 3

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.

  1. Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use α = 0.05.
  2. At 95% confidence, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West.

Part 2

Question 1

Assume you have noted the following prices for paperback books and the number of pages that each book contains.
Develop a least-squares estimated regression line.

  1. Compute the coefficient of determination and explain its meaning.
  2. Compute the correlation coefficient between the price and the number of pages. Test to see if x and y are related. Use α = 0.10.

Question 2

The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 8 years.

  1. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.
  2. Use the method of least squares to compute an estimated regression line between sales and advertising.
  3. If the company’s advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.
  4. What does the slope of the estimated regression line indicate?