Question

To study if high cholesterol levels are more common among men than among women, a sample of 244 men and a sample of 232 women were randomly selected. The cholesterol levels were measured and 74 men and 48 women had elevated levels. At α=0.05, can it be concluded that men are more susceptible to having higher levels of cholesterol?

Answer 1

Solution :

Given that,

n₁ = 244

x₁ = 74

Point estimate = sample proportion = ₁ = x₁ / n₁ = 0.303

n₂ = 232

x₂ = 48

Point estimate = sample proportion = ₂ = x₂ / n₂ = 0.207

The value of the pooled proportion is computed as,

= ( x₁ + x₂ ) / ( n₁ + n₂ )

= (74 + 48 ) / (244 + 232 )

= 0.256

1 - = 0.744

Level of significance = = 0.05

This a right(one)-tailed test.

The null and alternative hypothesis is,

Ho: p₁ = p₂

Ha: p₁ > p₂

Test statistics

z = (₁ - ₂ ) / *(1-) ( 1/n₁ + 1/n₂ )

= ( 0.303 - 0.267) / ( 0.256 * 0.744) (1/244 + 1/232 )

= 2.407

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 1.64

Since it is observed that z = 2.407 > = 1.64  , it is then concluded that the null hypothesis is rejected.

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 2.407)

= 0.008

The p-value is p = 0.008, and since p = 0.008 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that it be concluded that men are more susceptible to having higher levels of cholesterol, at the 0.05 significance level.