Question

A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement "Government should be more involved in oversight and regulation of reporting". Fifty-two (52) percent of the respondents agreed with the statement. Calculate the appropriate test statistic to test the claim that at least 50% of journalism majors agree with the statement.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p ≥ 0.50

H_a : p < 0.50

N = 400

= 0.52

P₀ = 0.50

1 - P₀ = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.52 -0.50 / [0.50(1-0.50) /400 ]

= 0.80

P(z > 0.80) = 1 - P(z < 0.80) =0.7881

P-value = 0.7881