Answer:
(a) $62.16
(b) Male: $15.00
Female: $10.06
(c) Confidence Interval for male expenditure is ($106.40, $136.40)
Confidence interval for female expenditure is ($49.18, $69.30)
Step-by-step explanation:
(a) Male expenditure
Sample mean = $135.67, sd=$35, n=40, Z=2.576
Population mean = sample mean - (Z×sd)/√n = 135.67 - (2.576×35)/√40 = 135.67 - 14.27 = $121.40
Female expenditure
Sample mean= $68.64, sd=$20, n=30, Z=2.576
Population mean = 68.64 - (2.576×20)/√30 = 68.64 - 9.40 = $59.24
$121.40 - $59.24 = $62.16
(b) Male: Error margin = (t-value × sd)/√n
Degree of freedom = n-1 = 40-1= 39. t-value corresponding to 39 degrees of freedom and 99% confidence level is 2.708
Error margin = (2.708×35)/√40 = 94.78/6.32 = $15.00
Female
Degrees of freedom = n-1 = 30-1 = 29. t-value is 2.756
Error margin = (2.756×20)/√30 = 55.12/5.48 = $10.06
(c) Male
Confidence Interval (CI) = (mean + or - error margin)
CI = 121.4 + 15.00 = $136.40
CI = 121.4 - 15.00 = $106.40
Confidence Interval is ($106.40, $136.40)
Female
CI = 59.24 + 10.06 = $69.30
CI = 59.24 - 10.06 = $49.18
Confidence Interval is ($49.18, $69.30)
