Question

In a survey, 14 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $12. Construct a confidence interval at a 99% confidence level.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 41

sample standard deviation = s = 12

sample size = n = 14

Degrees of freedom = df = n - 1 = 13

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,24 = 3.012

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

= 3.012 * (12 / 14)

= 9.660

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

- E < < + E

41 - 9.660 < < 41 + 9.660

31.340 < < 50.660

(31.340 , 50.660)