Question

In a survey, 15 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 $7. Construct a confidence interval at a 90% confidence level.

Give your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $48

sample standard deviation = s = $ 7

sample size = n = 15

Degrees of freedom = df = n - 1 =15-1=14

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.9 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,14 = 1.761

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

= 1.761 * (7 / 15)

= 3.2

The 90% confidence interval estimate of the population mean is,

- E < < + E

48 - 3.2 < < 48 + 3.2

44.8 < < 51.2

(44.8,51.2)