Question

A claim is made that the proportion of children who play a sport is less than 0.5. A sample is

taken of 500 children which finds that 40%

of them play sports.State your hypothesis and test

the claim at .1 significance.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p < 0.5

$\hat p$ = 0.40

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.40 - 0.5 / [$\sqrt$(0.5 * 0.5) / 500]

= -4.472

P-value = 0.0000

$\alpha$ = 0.01

P-value < $\alpha$

Reject the null hypothesis .

There is sufficient evidence to suggest that  proportion of children who play a sport is less than 0.5.