Question

8) An economic surveys 38 adults living is Townsburg about their salaries. The mean annual salaries for those surveyed was found to be x̄ = $43,551, with a standard deviation of $2,262.

a) Find a 90% confidence interval for the true mean annual salary of adults living in Townsburg.

b) Provide the right endpoint of the interval as your answer.

Round your answer to the nearest dollar.

Answer 1

a)

df = n - 1 = 38 - 1 = 37

From T table,

t critical value at 0.10 significance level with 37 df = 1.687

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

43551 - 1.687 * 2262 / sqrt(38) < < 43551 + 1.687 * 2262 / sqrt(38)

42932 < < 44170

90% C I is ( 42932 , 44170 )

b)

Right endpoint = 44170