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 $46 and standard deviation of $9. 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 = = $46

sample standard deviation = s = $9

sample size = n = 15

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

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.8 = 0.2

/ 2 = 0.2 / 2 = 0.1

t _/2,df = t_0.1,14 = 1.345

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

= 1.345 * (9 / 15)

= 3.1

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

- E < < + E

46 - 3.1 < < 46 + 3.1

42.9 < < 49.1

(42.9 , 49.1) A confidence interval at a 80% confidence level is ($42.9 , $49.1)