Question

Please do question by hand (not in R). Show enough work for me to understand. Thanks.

4. August, Hung, and Houck (1974) studied collagen metabolism in children deficient in growth hormone before and after growth hormone therapy. The data in Table 3.4 are the values of heat-insoluble hydroxyproline in the skin of children before and 3 months after growth hormone therapy. Can we conclude on the basis of these data that growth hormone therapy increases heat-Insoluble hydroxyproline in the skin? Table 3.4 Heat-Insoluble Hydroxyproline Micromoles per Gram of Dry Weight Child i Before After 2 3 4 5 6 7 349 425 400 533 520 362 490 628 574 463 427 427 435 449

Answer 1

Claim: Growth hormone therapy increases heat insoluble hydroxyproline in the skin.

That means difference(d) = After - Before is more, that is greater than 0

Therefore the claim is

Steps of hypothesis testing:

Step 1: To set the null and alternative hypothesis

The null and alternative hypothesis are,

Step 2: Test statistics

Here the sample of 7 is given so t test is applicable

The formula of t test statistics is,

Where

n - number of pairs = 7

Difference = After - Before

The differences are 76, 133, -158, 138, -111, 0, 14

Plug all the values in the formula of test statistics,

Step 3: Critical value

Here the alternative hypothesis contains > sign so the test is right tailed test.

Significance level (alpha) is not mentioned so take it as 0.05

So the critical value using the t table, see alpha 0.05 in one tail area and DF = 6, so the corresponding critical value is 1.943

Step 4: Decision

Decision rule: If t critical value > t test statistics then we fail to reject the null hypothesis otherwise reject the null hypothesis.

Here t critical value (1.943) is > t test statistics (0.303), so we fail to reject the null hypothesis.

Step 5: Conclusion

Here we fail to reject the null hypothesis that is not in favor of claim which is in alternative hypothesis.

There is no sufficient evidence to support the claim that, growth hormone therapy increases heat insoluble hydroxyproline in the skin.