The average expenditure on Valentine\'s Day was expected to be $100.89 ( USA Tod
ID: 3391248 • 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 $139, and the average expenditure in a sample survey of 33 female consumers was $67. Based on past surveys, the standard deviation for male consumers is assumed to be $32, and the standard deviation for female consumers is assumed to be $16. The z value is 2.576 .
Round your answers to 2 decimal places.
a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?
b. At 99% confidence, what is the margin of error?
c. Develop a 99% confidence interval for the difference between the two population means.
Explanation / Answer
a)
X1 = 139
X2 = 67
Thus, the point estimate is
X1 - X2 = 72 [ANSWER]
*********************
b)
Calculating the standard deviations of each group,
s1 = 32
s2 = 16
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 42
n2 = sample size of group 2 = 33
Thus, df = n1 + n2 - 2 = 73
Also, sD = 5.6690853
Note that
Margin of error = z*alpha/2 * sD
Thus,
Margin of error = 14.60259604 [ANSWER]
***********************
c)
Lower Bound = X - z(alpha/2) * sD
Upper Bound = X + z(alpha/2) * sD
where
alpha/2 = (1 - confidence level)/2 = 0.005
Thus,
X = sample mean = 72
z(alpha/2) = critical z for the confidence interval = 2.575829304
sD = standard error = 5.6690853
Thus,
Lower bound = 57.39740396
Upper bound = 86.60259604
Thus, the confidence interval is
( 57.39740396 , 86.60259604 ) [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.