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 $31 and standard deviation of $12. Construct a confidence interval at a 95% confidence level. Give your answers to one decimal place.

Answer 1

Solution :

Given that,

= 31

s = 12

n = 21

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,20 = 2.086

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

= 2.086 * (12 / 21)

= 5.5

The 95% confidence interval estimate of the population mean is,

- E < < + E

31 - 5.5 < < 31 + 5.5

25.5 < < 36.5

(25.5 , 31.5)