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

Answer:

Step-by-step 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:

$Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }$ ≈ 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:

$Z_{H_0}= \frac{0.60-0.45}{\sqrt{\frac{0.45*0.55}{30} } } = 1.6514$

I hope it helps!