Question

In a random sample of twelve ​people, the mean driving distance to work was 24.5 miles and the standard deviation was 5.2 miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a 90% confidence interval for the population mean μ.

Identify the margin of error.

Construct a 90​% confidence interval for the population mean.

Answer 1

Margin of error formula (for confidence interval for population mean)

90% confidence interval for the population mean

Given,

Number people in the random sample : Sample size : n =12

Mean driving distance to work : Sample mean : = 24.5

Sample standard deviation : s = 5.2

for 90% confidence level = (100-90)/100 = 0.10

/2 = 0.10/2 = 0.05

Degrees of freedom = n-1 = 12 -1 =11

t_0.05,,11 =  1.7959

Margin of error:

Margin of error = 2.6958

90% confidence interval for the population mean

Margin of error = 2.6958
90% confidence interval for the population mean = (21.8042 , 27.1958)