Question

A claim is made that the proportion of children who play sports is less than 0.5.The sample statistics include 1933 subjects with 30% saying that they play a sport. Test this claim. Write all five steps.Find the P-value for testing the manufacturers claim .

Answer 1

Given:

Number of sample, n = 1933

Sample proportion, = 0.30

Claim : The proportion of children who play sports is less than 0.5.

Hypothesis test:

The null and alternative hypothesis is

Ho : p= 0.5

Ha : p< 0.5

Test statistics ;

z = - p/√[p(1-p)/n]

= 0.30-0.5/√[0.5(1-0.5)/1933]

= -17.59

z = -17.59

P-value :

P-value = P(Z< -17.59) = 0.0000 ...(from z table)

Since P-value < = 0.05, we reject null hypothesis .

Decision : Reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that the proportion of children who play sports is less than 0.5.