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 are the null and alternative hypotheses for the test?

Answer 1

Here we have :

201 among 613 low-educated women (L) use contraceptives.

so nL = 613, xL = 201

Hence proportion of low educated women use contraceptives is :

  

= 0.33

Also we have , 228 out of 848 women with some education beyond high school (H) use contraceptives.

so nH = 848, xH = 228

Hence proportion of women with education beyond high school use contraceptives is :

  

= 0.27

Claim : Better-educated women are more likely to use contraceptives compared to low-educated women.

Hence the hypothesis are :

H0 : PL = PH v/s H1 : PL < PH

The test statistic is given by,

Where,

= 0.29

Hence the test statistic value is given by,

= -2.49

p value = p ( z < -2.49 )
= 0.0064 ------------( using excel formula "=norm.s.dist(-2.49,1)" )

Here p value < ( 0.05)

Hence we reject null hypothesis.

Conclusion :

There are sufficient evidence to support the claim that better-educated women are more likely to use contraceptives compared to low-educated women.