Question

A research company claims that no more than 55% of Americans regularly watch FOX News. You decide to test this claim and ask a random sample of 425 Americans if they watch this network regularly. Of the 425 sampled, 255 respond yes. Calculate the test statistic for the hypothesis test.

Answer 1

Answer: z(e) = 2.07

Step-by-step explanation:

1.-The problem is about a test of proportions. As research company claims than no more 55 % of Americans regularly watch Fox News

The null hypothesis is  H₀       P₀ ≤ 0.55       from 55%

And the alternative hypothesis is  Hₐ      Pₐ > .55

Is one tail test

2.-We have to specify significance level we assume our test will be for a significance level α = 5%  or α = 0,05

3.-Calculation of z (c) = ??  and z (e) = '??

For z (c) we find in z table the value of  z(c) = 1.64

For z (e) = ( P -P₀)/√p₀q₀/n     z(e) = 0.05 / √(0.55*0,45)/425                         z(e) = 0,05/ 0.02413    z(e) = 2.07

z(e) > z(c)  threfore z(e) is in the rejection zone . We reject null hyothesis