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A survey by American Express Spending reported that the average amount spent on a wedding gift...

A survey by American Express Spending reported that the average amount spent on a wedding gift for a close family member is $166. A random sample of 45 people who purchased wedding gifts for a close family member spent an average of $160.50. Assume that the population standard deviation is $38. Use a 95% confidence interval to test the validity of this report and choose the one statement that is correct.

a.

Because this confidence interval does include $166, the report by American Express Spending is not validated.
b.

Because this confidence interval does include $166, the report by American Express Spending is validated.
c.

Because this confidence interval does not include $166, the report by American Express Spending is not validated.
d.

Because this confidence interval does not include $166, the report by American Express Spending is validated.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 160.50

Population standard deviation = = 38

Sample size = n = 45

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * (38 / 45 )

= 11.10

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

- E < < + E

160.50 - 11.10 < < 160.50 + 11.10

149.40 < < 171.60

b)

Because this confidence interval does include $166, the report by American Express Spending is validated.

milcah answered 5 months ago
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