Question

A sports magazine claims that in a certain country, 45% of people like soccer A news channel asked 30 randomly selected people if they like playing soccer. Of those, 18 responded positively. To determine if 45% of the people like soccer in that country, the news channel conducted a hypothesis test as follows:

H0:p0=0.45
Hα:p0≠0.45
Find the test statistic for the given data. Round your answer to three decimal places.

Answer 1

Explanation:

Hello!

The parameter of interest is "the population proportion of people that like soccer A news channel"= p

The hypothesis are:

H₀: p = 0.45

H₁: p ≠ 0.45

To study the population proportion you have to use the approximation of the standard normal distribution:

`Z= \frac{p'-p}{\sqrt{(p(1-p))/(n) } }` ≈ N(0;1)

A sample of n=30 was taken and surveyed, 18 of those answered positively, then the sample proportion is:

p'= 18/30= 0.6

The statistic under the null hypothesis is:

`Z_(H_0)= \frac{0.60-0.45}{\sqrt{(0.45*0.55)/(30) } } = 1.6514`

I hope it helps!