Question

In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $7. Construct a confidence interval at a 90% confidence level.

Give your answers to one decimal place and Interpret your confidence interval in the context of this problem.

Answer 1

sample mean, xbar = 42
sample standard deviation, s = 7
sample size, n = 26
degrees of freedom, df = n - 1 = 25

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.708

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (42 - 1.708 * 7/sqrt(26) , 42 + 1.708 * 7/sqrt(26))
CI = (39.7 , 44.3)

We are 90% confident that the true population mean of the amount spent on the child's last birthday gift is between 39.7 and 44.3