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 $34 and standard deviation of $16. Construct a confidence interval at a 80% confidence level.

Give your answers to one decimal place.

_____ ± _____

Answer 1

Solution :

Given that,

= $34

s = $16

n = 21

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

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.2

/ 2 = 0.2 / 2 = 0.1

t /2,df = t0.1,20 = 1.325

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

= 1.325 * (16 / 21)

= 4.6

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

- E < < + E

34 - 4.6 < < 34 + 4.6

29.4 < < 38.6

(29.4,38.6)  

The 80% confidence interval 29.4 to 38.6