Question

(1 point) A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 278 students was x⎯⎯⎯ = 147 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 65 minutes in the population of all first-year students at this university. Use the survey result to give a 90% confidence interval for the mean study time of all first-year students.

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Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 147

σ = 65

n = 278

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 147 ± 1.6449*65/sqrt(278)

Confidence interval = 147 ± 6.4124

Lower limit = 147 - 6.4124 = 140.59

Upper limit = 147 + 6.4124 = 153.41

Confidence interval = (140.59, 153.41)

Confidence interval = 140.59 to 153.41