The average expenditure on Valentine\'s Day was expected to be $100.89 (USA Toda
ID: 3122749 • Letter: T
Question
The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 42 male consumers was $135.67, and the average expenditure in a sample survey of 38 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $36, and the standard deviation for female consumers is assumed to be $21.
What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
At 99% confidence, what is the margin of error (to 2 decimals)? Develop a 99% confidence interval for the difference between the two population means (to 2 decimals).
Develop a 99% confidence interval for the difference between the two population means (to 2 decimals).
Explanation / Answer
Point estimate is 135.67 - 68.64 = 67.03
Margin of error
ME = z * sqrt ( s1^2 / n1 + s2^2 / n2)
= 2.576 * sqrt ( 36^2 / 42 + 21^2/38)
= 6.516
CI = (x1 - x2 ) + / ME
= ( 135.67 - 68.64) + / - 6.516
= (60.514 , 73.546)
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