Question

A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1204 subjects with 30% saying that they play a sport.

Answer 1

The value of the test statistic is z= -13.88

To test the claim that the proportion of children who play sports is less than 0.5, you can conduct a hypothesis test. one can define the hypotheses:

• Null Hypothesis (H₀): The proportion of children who play sports is equal to or greater than 0.5. p≥0.5
• Alternative Hypothesis (H₁): The proportion of children who play sports is less than 0.5. p<0.5

So, based on the question:

Pcap= 0.3 ,p=0.5 ,q= 1-0.5= 0.5, n=1204

Z= (pcap- p) / √(p×q)/n

Z=( 0.3- 0.5) / √ (0.5 × 0.5)/1204

Z= -0.2/(√0.0002076)

Z= -13.88