Question

A researcher wishes to know if the data she has collected provide sufficient evidence to indicate a difference in mean serum uric acid level between normal individuals and individuals with Down' s syndrome. The data consist of serum uric acid readings on 12 individuals with Downâ€s syndrome and 15 normal individuals. The mean serum uric acid for individuals with Down's syndrome is 4.5 mg/100 ml and SD = 1 and the mean serum uric acid level for normal individuals is 3.4 mg/100 ml with SD = 1.5. Let α = 0.05.

1. Choose the correct name of the hypothesis being tested in this study. Alternative hypothesis

2. Is the alternative hypothesis being tested in this study directional or nondirectional? Nondirectional

3. Write the null and alternative hypotheses for this study.

   1. Null hypothesis: There is no difference in mean serum uric acid level between normal individuals and individuals with Down's syndrome.

   2. Alternative hypothesis: There is a difference in mean serum uric acid level between normal individuals and individuals with Down's syndrome.

4. What is the level of significance for this study? 5%

5. What would be the confidence level for this study? 95%

The researcher runs the analysis for this data, and she obtains a mean difference of 1.1 mg/100 ml in serum uric acid between the two groups with a CI of (0.1 - 2.1) and p-value = 0.0318.

6. Write your interpretation of the obtained confidence interval (0.1 - 2.1) using the confidence interval level you calculated in question 5. CI = 2.0

   1. ??????????

7. Based on the obtained p-value, is the difference in the mean serum uric acid between the two groups statistically significant or not? Why or why not? Yes, the difference is statistically significant because we reject the null hypothesis based off the concept of the p value being less that the alpha.

8. Assume that the researcher selects a significance level of 0.01 instead of 0.05 prior to data collection, and she obtained the same p-value = 0.0318 at the conclusion of the study, would the difference between the two means be statistically significant or not? Why or why not? No, the difference is statistically not significant because we fail to reject the null hypothesis based off the concept of the p value being greater than the alpha.

9. Using the new α = 0.01, would the new estimated confidence interval be narrower or wider than the original confidence interval with α = 0.05? Wider than the original

10. Do you think the study sample size is large enough? Why or why not?

    1. ??????

11. Assume that the researcher committed Type II error, what would their study conclusion possibly be?

    1. (this might be wrong)

    2. They would conclude that (having failed to reject a false null hypothesis): There is no difference in mean serum uric acid level between normal individuals and individuals with Down's syndrome.

How do I answer questions 6, 10, and 11?

Answer 1