Question

In a survey, 16 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 $15. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place. ±

Answer 1

Solution :

sample size = n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

t _/2,df = 2.947

Margin of error = E = t_/2,df * (s /n)

= 2.947 * (15 / 16)

Margin of error = E = 11.05

The 99% confidence interval estimate of the population mean is,

- E < < + E

39 - 11.05 < < 39 + 11.05

27.95‬ < < 50.05

(28, 50.1)

The 99% confidence interval is from 28 to 50.1