# Hypothesis testing!

• Dec 6th 2009, 06:04 PM
javax
Hypothesis testing!
Hello everyone!

A TV producer claims that 40 percent of parents watch his TV show. By the time when the show was transmitted, 100 parents were called on the phone, and it was found that 30 of them were watching the show. With $\displaystyle \alpha = 0.05$, was the producer right?

I'm confused with the standard deviation here! There isn't and I don't know how to find it!

THanks
• Dec 8th 2009, 10:45 AM
novice
Quote:

Originally Posted by javax
Hello everyone!

A TV producer claims that 40 percent of parents watch his TV show. By the time when the show was transmitted, 100 parents were called on the phone, and it was found that 30 of them were watching the show. With $\displaystyle \alpha = 0.05$, was the producer right?

I'm confused with the standard deviation here! There isn't and I don't know how to find it!

THanks

$\displaystyle p$ denotes the probability of parents watching the show.

Set the hypothesis using one-tailed test for the significance level of 0.05 as follows:

$\displaystyle H_0: p=0.4$ for the TV producer's claim is correct.
$\displaystyle H_1: p < 0.4$ for the claim is false.

If $\displaystyle z_c < z_{0.05}$ we can reject the hypothesis.

$\displaystyle \mu = NP = 100 (0.4)=40$ and $\displaystyle \sigma = \sqrt{Npq}=\sqrt{(100)(0.4)(0.6)}=4.90$

$\displaystyle z_c = \frac{30-40}{4.90}=-2.04 < z_{0.05}$

Based on the samples, using one-tailed test, we can reject the hypothesis at significance level of 0.02. The evidence indicates almost overwhelmingly that the TV producer's claim is false.