The Pew Research Center claims that more than 55 of American

The Pew Research Center claims that more than 55% of American adults regularly watch a network news broadcast. You decide to test this claim and ask a random sample of 425 Americans whether they regularly watch a network news broadcast. Of the 425 Americans, 255 responded yes. At = 0.05, is there enough evidence to support the claim?

Solution

Given that the Pew Research Center claims that more than 55% of Americans adults regularly watch a network news broadcast.

Here we have to test the hypothesis that,

H0 : p = 55% = 0.55 Vs H1 : p > 0.55

q = 1 - p = 1 - 0.55 = 0.45

where p is the population proportion.

n = number of Americans whether they regularly watch a network news broadcast = 425

x = number of Americans who responded yes = 255

p^ =sample proportion = x / n = 255 / 425 = 0.6

alpha = 0.05

The test statistic for testing proportion is,

z = (p^ - p) / sqrt [pq/n]

= (0.6 - 0.55) / sqrt [ (0.55*0.45) / n ]

z = 0.05 / 0.02413 = 2.0719

Critical value we can find by using EXCEL:

Syntax :

=normsinv (probability)

probability = 1 - alpha = 1 - 0.05 = 0.95

critical value = 1.645

z > critical value

Reject H0 at 5% level of significance.

Pew Research Center claims that more than 55% of Americans adults regularly watch a network news broadcast.