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

P1 :- Proportion of women with some education beyond high school.

P2 :-  Proportion of women with some education below high school.

To Test :-
H0 :- P1 = P2
H1 :- P1 > P2

p̂1 = 228 / 848 = 0.2689
p̂2 = 201 / 613 = 0.3279

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 228 + 201 ) / ( 848 + 613 )
p̂ = 0.2936
q̂ = 1 - p̂ = 0.7064
Z = ( 0.2689 - 0.3279) / √( 0.2936 * 0.7064 * (1/848 + 1/613) )
Z = -2.4448 ≈ -2.44

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.05) = 1.645 ( From standard normal table )
Z < Z(α) = -2.4448 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > -2.4448 )  = 1 - 0.0072 = 0.99227
Reject null hypothesis if P value < α = 0.05
Since P value = 0.9927 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0 |

There is sufficient evidence to support the claim that women with some education beyond high school are more likely to use contraceptives compared to women with an education level at or below a high school level.