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 $37 and standard deviation of $20. Construct a confidence interval at a 99% confidence level.

Give your answers to one decimal place.

±±

Interpret your confidence interval in the context of this problem.

Answer 1

Solution :

Given that,

= 37

s = 20

n = 14

Degrees of freedom = df = n - 1 =14- 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 = t0.005,13 =3.012

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

= 3.012* (20 / 14)

= 16.10

Margin of error =16.10

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

- E < < + E

37 - 16.10 < < 37 + 16.10

20.90 < < 53.10

(20.90,53.10 )