Question

In a survey, 19 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $44 and standard deviation of $16. Construct a confidence interval at a 98% confidence level.

Give your answers to one decimal place.

__________± _____________

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 44

Population standard deviation = = 16

Sample size = n = 19

At 99% confidence level the z is ,

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576* (16 / 19 )

= 9.5

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

- E < < + E

44 - 9.5 < < 44 + 9.5

34.5 < < 53.5

( 34.5 , 53.5 )