Answer
We fail to reject the Null Hypothesis. There is not enough evidence to suggest that the proportion of male siblings is less than 0.51 in a family where one child has SLE.
Work Step by Step
Here we have: $H_{o}$: μ = 0.51, $H_{a}$: μ < 0.51, n = 194, $\hat p = 0.474$, p = 0.51
Verifying model requirements:
np(1-p) = 194 x 0.51 (1 - 0.51) = 48.48 > 10
$z = \frac{0.474 - 0.51}{\sqrt \frac{0.51 (1 - 0.51)}{194}} = \frac{-0.036}{0.0359} = -1$
$P (z \lt -1) = 0.1587 \gt 0.05$
Thus we do not reject the null hypothesis.
