Question

In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $48 and standard deviation of $19. Construct a confidence interval at a 99% confidence level.

Give your answers to one decimal place.

Answer 1

Solution :

sample size = n = 21

Degrees of freedom = df = n - 1 = 20

t /2,df = 2.845

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

= 2.845 * (19 / 21)

Margin of error = E = 11.8

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

- E < < + E

48 - 11.8 < < 48 + 11.8

36.2 < < 59.8

(36.2, 59.8)