Question

In: Statistics and Probability

In a survey, 10 people were asked how much they spent on their child's last birthday gift.

In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $38 and standard deviation of $8. Construct a confidence interval at a 98% confidence level.

Expert Solution

= 38

s = 8/

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t_/2,df = t_0.01,9 =2.821

Margin of error = E = t_/2,df * (s /√n)

= 2.821 * (8 / √10) = 7.1

The 98% confidence interval estimate of the population mean is,

- E < < + E

38 - 7.1 < < 38 + 7.1

30.9 < < 45.1

(30.9, 45.1 )

orchestra answered 2 years ago

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