Question

In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $50 and standard deviation of $8. Construct a confidence interval at a 80% confidence level.

Give your answers to one decimal place.

_____ ± _____

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 50

sample standard deviation = s = 8

sample size = n = 32

Degrees of freedom = df = n - 1 =32-1=31

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.8 = 0.2

/ 2 = 0.2 / 2 = 0.1

t /2,df = t0.1,31 = 1.309

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

= 1.309 * (8 / 32)

Margin of error = E = 1.9

The 80% confidence interval estimate of the population mean is,

- E <  < + E

50 - 1.9 < < 50 + 1.9

48.1 <  < 51.9

(48.1,51.9)