Question

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, conclusion in words)

Answer 1

Answer on Question #63325 – Math – Statistics and Probability

Question

Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, conclusion in words).

Solution

The null hypothesis $H_0: \mu_1 = \mu_2$

The alternative hypothesis $H_a: \mu_1 > \mu_2$.

It is given that $\bar{x}_d = 9$, $s_d = 24.24$.

Test statistic:

$$t = \frac{\bar{x}_d}{\frac{s_d}{\sqrt{n}}} = \frac{9}{\frac{24.4}{\sqrt{10}}} = 1.17.$$

P-value for $t = 1.17$, degrees of freedom $df = 10 - 1 = 9$,

level of significance $\alpha = 0.05$, one-tailed test:

$$p = 0.136025$$

Since the P-value (0.136025) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Thus we conclude that cholesterol levels were not significantly lowered by using low-fat diet for 12 weeks at 0.05 level of significance.

Answer: cholesterol levels were not significantly lowered by using low-fat diet for 12 weeks at 0.05 level of significance.

www.AssignmentExpert.com