Q1.5: Interval estimation – Applied Regression Modeling, 3rd edition

Answer the following questions based on Section 1.5: Interval estimation.

Suppose we have sampled 25 observations and our sample mean is 5.8 and our sample standard deviation is 2.5. Note that the 95^th percentile of a t-distribution with 24 degrees of freedom is 1.711, and the 97.5^th percentile is 2.064. Use this information to answer the following questions.

1.

Calculate the upper bound of a 95% confidence interval for the mean. Write a number rounded to three decimal places.

2.

Calculate the lower bound of a 95% confidence interval for the mean. Write a number rounded to three decimal places.

3.

Calculate the confidence level of a confidence interval for the mean that is between 4.9445 and 6.6555. Express as a percentage by writing a whole number.

4.

Which of the following is the correct interpretation of a 95% confidence interval for the mean that goes from 4.768 to 6.832?

The probability that the sample mean is between 4.768 and 6.832 is 0.95.

The probability that the population mean is between 4.768 and 6.832 is 0.95.

Under repeated sampling, 95% of such confidence intervals would contain the population mean.

Under repeated sampling, the population mean would be between 4.768 and 6.832 95% of the time.

5.

Which of the following will result in a wider confidence interval for the mean? Select all that apply.

Increased level of confidence.

Increased sample mean.

Increased sample standard deviation.

Increased sample size.

Applied Regression Modeling

3rd edition

Iain Pardoe