Question

In a random sample of 25 ​people, the mean commute time to work was 30.6 minutes and the standard deviation was 7.2 minutes.

Assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean μ.

What is the margin of error of μ​? Interpret the results.

1. The confidence interval for the population mean μ is (_,_)

2. The margin of error of μ is __

3. Interpret the results.

A.It can be said that 99​% of people have a commute time between the bounds of the confidence interval.

B.With 99​% ​confidence, it can be said that the commute time is between the bounds of the confidence interval.

C.With 99​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.Your answer is correct.

D.If a large sample of people are taken approximately 99​% of them will have commute times between the bounds of the confidence interval.

Answer 1

95​% confidence interval

The confidence interval for mean is obtained using the formula,

From the data values,

The t critical value is obtained from t distribution table for significance level = 0.10 and degree of freedom = n -1 = 25 - 1 = 24.

Margin of error

The margin of error of error for the mean is,

Interpretation:

Correct Answer:C.With 99​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Explanation: For 99% confidence interval, the 99% of the time true population mean will lie in this range