Question

In a survey, 48 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $51 and standard deviation of $2.

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

given data are:-

sample mean () = 51

sample sd (s) = 2

sample size (n) = 48

here, as the sample sd (s) is known, we will use t distribution.

degrees of freedom = (n-1) = (48-1 )= 47

t critical value for df = 47,alpha=0.05, both tailed test be :-

[ using t distribution table ]

the 95% confidence interval to estimate the mean amount of money parents spend on their child's birthday gift is:-

interpretation:-

we can be 95% confident that the true mean amount of money parents spend on their child's birthday gift will be within $ 50.42 and $ 51.58

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