Question

As a newly hired manager of a company that provides cell phone service, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line phones. How many adults must you survey? Assume that you want to be 90% confident that the sample percentage is within 4 percentage points of the true population percentage.

In a test of effectiveness of garlic for lowering cholesterol, 47 subjects were treated with Garlicin, which is garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have a mean of 3.2 and a standard deviation of 18.6.

Answer 1

1)

Answer:

Sample size = 423

Explanation:

The sample size is obtained using the formula,

Where,

Let  

The margin of error is 4%, i.e

For a 90% confidence interval, the z critical value is obtained from the standard normal distribution table,

Now,

2)

Since we are doing repeated measures on the same subject, the paired sample t-test is used to test the following hypothesis

Hypothesis:

The null and alternative hypothesis for the test is defined as

where the is mean difference between before and after LDL cholesterol level.

This is a one-tailed test.

Let the significance level = 0.05

Test statistic

The t-statistic is obtained using the formula,

From the data values,

P-value

The P-value for t = 1.1795 is obtained from t-distribution table for the degree of freedom = n - 1 = 46 and one-tailed alternative hypothesis,

Conclusion:

Since the p-value is greater than 0.05 at a 5% significance level, the null hypothesis is not rejected hence there is not sufficient evidence to conclude that the garlic is effective in lowering cholesterol level.