Question

Female 1, Male 0

Find the 95% confidence interval for both samples of female and male

		Total Debt	Random
18	0	$     4,685.60	0.971648
19	0	$     5,021.83	0.675106
22	0	$     5,184.00	0.428184
24	0	$     4,799.90	0.358585
28	0	$     2,290.95	0.416605
43	1	$     2,998.93	0.308098
44	1	$     3,627.81	0.692047
45	1	$     5,209.66	0.834437
46	1	$     2,981.50	0.585422
49	1	$     3,643.52	0.724077

Answer 1

The formula for estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

Here we have consider total debt is our sample column.

For Male-

Calculation

M = 3692.284
t = 1.96
s_M = √(907.5955²/5) = 405.89

μ = M ± Z(s_M)
μ = 3692.284 ± 1.96*405.89
μ = 3692.284 ± 795.52791

You can be 95% confident that the population mean (μ) falls between 2896.75609 and 4487.81191.

For Female-

Calculation

M = 3678.563
t = 1.96
s_M = √(2056.378²/5) = 919.64

μ = M ± Z(s_M)
μ = 3678.563 ± 1.96*919.64
μ = 3678.563 ± 1802.46167

You can be 95% confident that the population mean (μ) falls between 1876.10133 and 5481.02467.