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# Grantham University Statistics Confidence Interval Estimate Questions

Grantham University Statistics Confidence Interval Estimate Questions.

# Assignment Part 1

## Question 1

In a poll of 600 voters in a campaign to eliminate non-returnable beverage containers, 210 of the voters were opposed. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill.

Question 2

A random sample of 87 airline pilots had an average yearly income of \$99,400 with a standard deviation of \$12,000.

If we want to determine a 95% confidence interval for the average yearly income, what is the value of t?

Develop a 95% confidence interval for the average yearly income of all pilots.

## Question 3

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds.

Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.

Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

## Question 4

A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.7 to 12.3 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.28, determine the size of the sample.

# Assignment Part 2

## Question 1

Professor Nord stated that the mean score on the final exam from all the years he has been teaching is a 79%. Colby was in his most recent class, and his class’s mean score on the final exam was 82%. Colby decided to run a hypothesis test to determine if the mean score of his class was significantly greater than the mean score of the population. α = .01.

What is the mean score of the population?

What is the mean score of the sample?

Is this test one-tailed or two-tailed? Why?

What is the null hypothesis in this case?

If p = 0.29, should Colby reject or fail to reject the null hypothesis?

What should Colby’s statement of conclusion be? (This circles back to what is being tested).

The next two ask you do to a hypothesis test. Remember, hypothesis tests follow a series of steps. They are not just a computer printout. Make sure if you use a computer printout, you identify which parts of the printout apply to the problem. All of the parts of the printout will NOT apply.

Question 2

A sample of 22 account balances of a credit company showed a mean customer balance of \$4,300, but the marketing manager claimed that the mean balance for the population was \$4450. The marketing manager did NOT have the population standard deviation, but the sample standard deviation was found to be \$400. Use the p-value approach to conduct a full hypothesis test(all steps) that can be used to determine whether the mean of all account balances is significantly different from \$4440. Let α = .05.

## Question 3

A sample of 150 homes for sale in ABC City showed a mean asking price of \$233,000, but the city claimed that the mean asking price for the population was \$255,000. The population standard deviation of all homes for sale was \$11,000. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean asking price is significantly less than \$255,000. Let α = .10.

## Question 4

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

 State Voters Surveyed Voters in favor of Democratic Candidate Alabama 710 352 Mississippi 915 480

We want to determine whether or not the PROPORTIONS of voters favoring the Democratic candidate were the same in both states. In other words, is the first proportion (p1) the same as (p2)? What formula, from this week’s Notations and Symbols, would be applicable in the hypothesis test? (Notice you are not doing a hypothesis test – you are saying which formula applies).

# Assignment Part 3

## 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.

Compute the coefficient of determination and explain its meaning.

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.

Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.

Use the method of least squares to compute an estimated regression line between sales and advertising.

If the company’s advertising expenditure is \$400,000, what are the predicted sales? Give the answer in dollars.

What does the slope of the estimated regression line indicate?

Grantham University Statistics Confidence Interval Estimate Questions

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