Question

In a recent Super Bowl, a TV network predicted that 31 % 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 120 people who saw the commercials and found that 40 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:
1. H0: p = 0.53 Ha: p ≠ 0.53
2. H0: p = 0.53 Ha: p ≠ 0.53
Calculate the test statistic, rounded to 3 decimal places.

Answer 1

Answer:

-4.317

Step-by-step explanation:

The z test statistic for testing of 1-proportion can be computed as

$z=\frac{phat-p}{\sqrt{\frac{pq}{n} } }$

We know that

phat=x/n.

We know that x=40 and n=120.

Thus,

phat=40/120=0.3333

p=hypothesized proportion=0.53

q=1-p=1-0.53=0.47

So, required z-statistic is

$z=\frac{0.3333-0.53}{\sqrt{\frac{0.53(0.47)}{120} } }$

$z=\frac{-0.1967}{ 0.04556 }$

z=-4.317.

Thus, the required test statistic value for given hypothesis is z=-4.317.