1. ## Hypothesis Testing

"A manufacturer claims that 20% of the public preferred her product. A sample of 100 persons is taken to check her claim. It is found that 8 of these 100 persons preferred her product. Using the 0.05 level of significance test her claim (perform a two-sided test), and Find the p-value and explain what it means."

I think I understand what to do, but I don't get how to find the standard deviation for this sample.. After that, I know I'm supposed to create a Z-score, and see if it is in the rejection region, but without the SD, I can't get anywhere. I tried to assume this was a binomial distribution, and got SD = sqrt(npq), but the answer comes to accepting the H0 hypothesis, which is ridiculous.

2. ## Re: Hypothesis Testing

Originally Posted by limddavid
"A manufacturer claims that 20% of the public preferred her product. A sample of 100 persons is taken to check her claim. It is found that 8 of these 100 persons preferred her product. Using the 0.05 level of significance test her claim (perform a two-sided test), and Find the p-value and explain what it means."

I think I understand what to do, but I don't get how to find the standard deviation for this sample.. After that, I know I'm supposed to create a Z-score, and see if it is in the rejection region, but without the SD, I can't get anywhere. I tried to assume this was a binomial distribution, and got SD = sqrt(npq), but the answer comes to accepting the H0 hypothesis, which is ridiculous.

Under the null hypothesis the number who prefer the product in a sample of 100 has a binomial distribution B(100,0.2).

CB

3. ## Re: Hypothesis Testing

So, simulating the actual test as a binomial distribution b(100,0.08), the expected value is 8. Also, under the null hypothesis, the expectation is 20, and standard deviation is 4. So, the Z score would be (8-20)/(4/sqrt(100))? That gives me a P(Z<-30), which would clearly reject the null hypothesis.

4. ## Re: Hypothesis Testing

I used the normal approximation and got a test stat of -3, not 30.
So the approximate p-value is

$\displaystyle 2P(Z<-3)$

5. ## Re: Hypothesis Testing

got it. I guess since i'm not working with the mean, I dont need to include the sqrt(100) at the bottom. thank you!