Question

In a survey, 39 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $40 and standard deviation of $4.

Calculate, state, and interpret a 95% confidence interval to estimate the mean amount of money parents spend on their child's birthday gift. Round to the nearest 100th where necessary.

Answer 1

Solution :

Given that,

Z$\alpha$/2 = Z0.025 = 1.96

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 1.96 * ( 4 /  $\sqrt$39 )

= 1.26

At 95% confidence interval estimate of the population mean is,

$\bar x$  ± E

= 40  ± 1.26

= ( $ 38.74, $ 41.26 )

We are 95% confident that the true mean amount of money parents spend on their child's birthday gift between $ 38.74 and $ 41.26.