Question

In a random sample of 100 viewers, 72% had a favourable impression of a new TV ad campaign. (a) Test the hypothesis that fewer than 80% of the population of all viewers have a favourable

view of the ad campaign. Use the .05 level of significance. Explain your conclusion.
(b) Construct a 95% confidence interval for the proportion of the population of all viewers who

have a favourable view of the ad campaign. Interpret your results.

Answer 1

Step 1:

Ho: p ≥ 0.80

Ha: p < 0.80

Null hypothesis states that the proportion of viewers having a favourable impresison of a new TV campaign is greater than or equal to 0.80

Alternative hypothesis states that the proportion of viewers having a favourable impresison of a new TV campaign is less than 0.80

Step 2 Test statistics

x = 72

n = 100

z = -2.00

Critical Value of Z (Left Tailed): - 1.65

As z stat falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that proportion of viewers having a favourable impresison of a new TV campaign is less than 0.80

(b)

CI = 0.72 +/- 0.0880

CI = 0.6320 , 0.8080

We are 95% confident that the proportion of viewers having a favourable impresison of a new TV campaign is between 0.6320 , 0.8080