In a survey, 31 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $39 and standard deviation of $9. Construct a confidence interval at a 90% confidence level. Give your answers to one decimal place.

Answer: u = (41.659, 36.341)

Step-by-step explanation:

Constructing a 90% confidence interval for mean is given by the formulae below.

u = x + Zα/2 * σ/√n ... This is the upper limit

u = x - Zα/2 * σ/√n ... This is the lower limit.

u = population mean

x = sample mean = 39

σ = population standard deviation = 9

Zα/2 = Z score for a two tailed test with an a level of significance = 1.645 (for 90% confidence level)

Upper limit

u = 39 + 1.645 * (9/√31)

u = 39 + 1.645 * (1.616)

u = 39 + 2.6590

u = 41.659

Lower limit

u = 39 - 1.645 * (9/√31)

u = 39 - 1.645 * (1.616)

u = 39 - 2.6590

u = 36.341