Question

In a recent Super Bowl, a TV network predicted that 67% 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, an advertising Group sampled 69 people who saw the commercials and found that 47 of them said they would watch one of the television shows.

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

Ho: p= 0.67

Ha: p< 0.67

Calculate the test statistic, rounded to 3 decimal places, show work!

Z=____

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.67

H_a : p < 0.67

= x / n = 47 / 69 = 0.68

P₀ = 0.67

1 - P₀ = 1 - 0.67 = 0.33

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.68 - 0.67 / [(0.67 * 0.33) / 69]

Test statistic = z = 0.177