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 $63 and standard deviation of $19.

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 :

The 95% confidence interval to estimate the population mean is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and t(0.05/2, n - 1) is critical t value to construct 95% confidence interval.

We have,  x̅ = $63, s = $19, n = 39

Using t-table we get, t(0.05/2, 39 - 1) = 2.0244

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

The 95% confidence interval to estimate the mean amount of money parents spend on their child's birthday gift is ($56.84, $69.16).

Interpretation :

We are 95% confident that, the mean amount of money parents spend on their child's birthday gift lies between $56.84 and $69.16.

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