Question

1. A random sample of 600 high school boys showed that 50 had taken diet pills during the past 30 days to lose weight. The researhcer wants to test if less than 10 % of all high school boys who take diet pills will lose weigt. A)state the null hypothesis and alternative hypothesis. B)Verify necessary data necessary data conditions for a z-statisitc. Calculate z statistic. e) find the p value. Are the result statistically significant at a significant level a=0.05?

Answer 1

Here, we have sample proportion, $p=50/600=0.083$ and the sample size, $n=600$

Suppose the null hypotheses, $H_0: P=0.10$

Alternate hypotheses, $H_1:P<0.10$

First we will calculate the standard deviation of the sampling distribution,

$\sigma=\sqrt{P*(1-P)/n}$

where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size.

$\sigma=\sqrt{(0.10*0.90)/600}$

$=\sqrt{0.09/600}$

$=0.0122$

Since the data are simple random sample from the population of interest, we can use Z-test.

$z=(p-P)/\sigma$

$=(0.083-0.10)/0.0122$

$=-0.017/0.0122$

$=-1.39$

Since we have a one tailed test, the P-value is the probability that the z-score is less than -1.39.

We will use normal distribution table to find $P(z<-1.39)=0.082$ .

Thus, P-value = 0.082

Since the p-value is greater than the significance level, $\alpha=0.05$ , we cannot reject the null hypothesis.

So, there is not strong evidence to say that less than 10 % of all high school boys who take diet pills will lose weight.