Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the women,
x = 702
n1 = 798
p1 = 702/798 = 0.88
For the men
x = 802
n2 = 940
p2 = 802/940 = 0.85
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.88(1 - 0.88)/798 + 0.85(1 - 0.85)/940]
= 1.96 × √0.00026796913
= 0.032
Confidence interval = (0.88 - 0.85) ± 0.032
= 0.03 ± 0.032
Lower boundary = 0.03 - 0.032 = - 0.002
Upper boundary = 0.03 + 0.032 = 0.062
The proportion of all working women who consider job security very or extremely important is higher than that of men and we are 95% confident that the population difference lies between - 0.002 and
0.062
