Question

It is believed that the women with some education beyond high school (H) are more likely to use contraceptives compared to women with an education level at or below a high school level (L). A study was conducted to test this claim and found out that 201 among 613 low-educated women (L) use contraceptives and 228 out of 848 women with some education beyond high school (H) use contraceptives. Does it appear that better-educated women are more likely to use contraceptives compared to low-educated women? Conduct a test of hypothesis at 5% level of significance. What is the test statistic? (Hint: Round sample proportions to four decimal places.)

Answer 1

p_L : proportion of low-educated women use contraceptives

p_H : proportion of women with some education beyond high school use contraceptives

Null hypothesis : H_o : p_H - p_L = 0

Alternate hypothesis : H_a : p_H - p_L > 0

right tailed test

Given
n1 : Sample Size of  women with some education beyond high school	848
n2 : Sample Size of low educated women	613
x1 : Number of women with some education beyond high school who use contraceptives	228
x2 Number of low educated women who use contraceptives	201
$\widehat{p}_{1}$ : Sample Proportion of women with some education beyond high school who use contraceptives	0.2689
$\widehat{p}_{2}$: Sample Proportion of low educated women who use contraceptives	0.3279
Level of significance : $\alpha$	5%

Test Statistic : Z= – Pi - P2 Pill-pi) – P2(1-pa) 122

0.2689 -0.3279 *0.2689(1.0.2689), 0.327911-0.3279} 818 -0.059 0.0243 = -2.4262 0.26B\1 十 613

For right tailed test:

p-Value = P(Z > Zstat) = P(Z > -2.4262)

P(Z > -2.4262) = 1- P(Z < -2.4262) = 1-0.0076 = 0.9924

p-value = 0.9924

As P-Value i.e. is greater than Level of significance i.e (P-value:0.9924 > 0.05:Level of significance); Fail to Reject Null Hypothesis

There is not enough evidence to conclude that proportion of women with some education beyond high school use contraceptives is more than the proportion of low educated women use contraceptives

There is not enough evidence that better-educated women are more likely to use contraceptives compared to low-educated women