Question

In: Statistics and Probability

In a survey, 39 people were asked how much they spent on their child's last birthday...

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 $45 and standard deviation of $14.

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.

Expert Solution

Solution

Given that,

= 45

= 14

n = 39

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960 * (14 / $\sqrt$ 39 )

= 4.39

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

- E < < + E

45 - 4.39 < < 45 + 4.39

40.61 < < 49.39

(40.61 , 49.39)

orchestra answered 1 year ago

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