Module 07 Questions
1. Cortisol level determinations were made on two samples of women at childbirth. Group 1 subjects underwent emergency cesarean section following induced labor. Group 2 subjects delivered by either cesarean section or the vaginal route following spontaneous labor. The samples sizes, mean cortisol levels, and standard deviations were as follows:
Sample N Mean St. Dev
1 10 435 61
2 12 645 88
Assume that the cortisol levels are approximately normally distributed in each group.
(a) Do these data provide sufficient evidence to indicate a difference in the mean cortisol levels in the populations represented? Perform a hypothesis test at the 5% significance level.
Be sure to provide the following:
- Define the parameter(s) of interest.
- State the null and alternative hypotheses.
- State the significance level.
- State what type of test you will perform, why you chose to use that test, and provide a check for any necessary assumptions.
- State your test statistic and its null distribution.
- Compute the test statistic BY HAND. Make a decision to reject or fail to reject based on either a p-value or by comparing the test statistic to a critical value (you can choose whichever you prefer).
- State your conclusion in the context of the problem.
(b) Construct and interpret a 95% confidence interval for the difference in the population means.
2. The Bayley Scales of Infant Development yield scores on two indices – the Psychomotor Development Index (PDI) and the Mental Development Index (MDI) – that can be used to assess a child’s level of functioning at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study investigating the development and neurologic status of children who had undergone reparative heart surgery during the first three months of life, the Bayley Scales were administered to a sample of one-year-old infants born with congenital heart failure. The children had been randomized to one of two different treatment groups, known as “circulatory arrest” and “low-flow bypass”.
The groups differed in the specific way in which the reparative surgery was performed. Unlike circulatory arrest, low-flow bypass maintains continuous circulation through the brain; although it is felt to be preferable by some physicians, it also has its own associated risk of brain injury.
The data for this study are in the dataset “Heart” in Canvas. PDI scores are saved under the variable name pdi, MDI scores under mdi, and indicators of treatment group under trtment. For this variable, 0 represents circulatory arrest and 1 is for low-flow bypass.
At the 5% significance level, test the null hypothesis that the mean MDI score at one year of age for the circulatory arrest treatment group is equal to the mean MDI score for the low-flow group. Also provide and interpret the corresponding 95% confidence interval.
- Define the parameter of interest.
- State the null and alternative hypotheses.
- State the significance level.
- State what type of test you will perform and why you chose to use that test.
- State and check any necessary assumptions. (Even if the sample sizes are sufficient, check normality of the values in the two groups.)
- State your test statistic and its null distribution.
- Give the output of the hypothesis test from R. Verify the calculation of the test statistic by hand. You do not have to verify the P-value by hand. You also do not have to state the decision rule.
- State your conclusion in the context of the problem. Be sure to include the P-value and confidence interval.
3. A crossover study was conducted to investigate whether oat bran helps to lower serum cholesterol levels in hypercholesterolemic males. Fourteen such individuals were randomly placed on a diet that included either oat bran or corn flakes; after two weeks, their low-density lipoprotein (LDL) (in mmol/l) cholesterol levels were recorded. Each man was then switched to the alternative diet. After a second two-week period, the LDL cholesterol level of each individual was again recorded. We want to see if oat bran lowers cholesterol more than cornflakes. The data is in “Oatbran” in Canvas. Perform the appropriate test using R.
- Define the parameter of interest.
- State the null and alternative hypotheses.
- State the significance level.
- State what type of test you will perform and why you chose to use that test.
- State and check any necessary assumptions.
- State your test statistic and its null distribution.
- State your decision rule.
- Give the output of the hypothesis test from R. Verify the calculation of the test statistic by hand. You do not have to verify the P-value by hand.
- State your conclusion in the context of the problem. Be sure to include the P-value.
Module 08 Questions
4. At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth. The data are for January, May, and September
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