Question

In a recent Super Bowl, a TV network predicted that 46 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 101 people who saw the commercials and found that 41 of them said they would watch one of the television shows.

Suppose you are have the following null and alternative hypotheses for a test you are running:

H 0 : p = 0.46

H a : p ≠ 0.46

Calculate the test statistic, rounded to 3 decimal places z =

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.46

H_a : p 0.46

= x / n = 41 / 101 = 0.406

P₀ = 0.46

1 - P₀ = 1 - 0.46 = 0.54

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.406 - 0.46 / [(0.46 * 0.54) / 101]

Test statistic = z = -1.089