Answer to Question #217143 in Statistics and Probability for Dani

Question

In a survey of 500 infants chosen at random, it is found that 240 are girls. Are boy and girl births equally likely according to this survey (use α = 0.05)

Answer 1

H₀: there is no significant difference between boy births and girl births

H₁: there is a significant difference between boy births and girl births

The probability of girl birth $= p =\frac{1}{2}=0.5$

The probability of boy birth $= q = \frac{1}{2}=0.5$

$n=500 \\ \sqrt{ \frac{pq}{n} }= \sqrt{ \frac{0.5 \times 0.5}{500} }=0.02236$

The observed sample proportion of girl birth

$\hat{p}= \frac{240}{500}=0.48$

The test-statistic:

$Z = \frac{\hat{p}-p}{\sqrt{ \frac{pq}{n} }} \\ Z = \frac{0.48-0.5}{0.02236}= -0.894 \\ α=0.05 \\ Z_{crit}= 1.96 \\ Z < Z_{crit}$

Accept H₀.

There is enough evidence to conclude that here is no significant difference between boy births and girl births at the 0.05 significance level.