Question

In a recent Super Bowl, a TV network predicted that 47 % 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 103 people who saw the commercials and found that 49 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:

H0:p=0.47
Ha:p<0.47

Calculate the test statistic, rounded to 3 decimal places

z=

Answer 1

The null and alternative hypothesis are given as-

• Null hypothesis,
• Alternative hypothesis,

Now the information is given for the randomly selected people who saw the commercial and out of which 49 said that they would watch one of the television shows.

The formula for calculating the test statistic is given by-

where,

the null- hypothesized value for the population proportion p.

sample proportion, i.e.,

sample size

Calculation of the test statistic:

So the test statistic is calculated as