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TTTT 1022 Data Analysis

Exercise 1

1.  Assume that the following two samples are independent simple random samples selected from normally distributed populations and the population standard deviations are equal. Use the traditional method and P -value method.

A researcher was interested in comparing the quiz scores between students participating in collaborative and students participating in individual learning activities. Independent random samples of  students from each activity yielded the following scores:

Use a 0.10 significance level to test the claim that the mean quiz scores of students in collaborative activity is higher from the individual activity.

2. Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations and the population standard deviations are equal. Use rejection region method and P -value method as indicated.

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure, measured in mm Hg, by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment group is from a population with a smaller mean than the control group. Use the traditional method of hypothesis testing.

Treatment Group  Control Group

n1 = 25 n2 = 28

x1 = 189.1 x2 = 203.7

s1 = 38.7  s2 = 39.2

3.  Is Blood Pressure the Same for Both Arms? Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman (based on data from “Consistency of Blood Pressure Differences Between the Left and Right Arms,” by Eguchi, et al., Archives of Internal Medicine, Vol. 167). Use a 0.05 significance level to test for a difference between the measurements from the two arms. What do you conclude?

Right arm        102         101    94    79    79

Left arm          175        169    182   146   144

4. Does Your Body Temperature Change During the Day? Listed below are body temperatures (in oF) of subjects measured at 8:00 AM and at 12:00 AM (from University of Maryland physicians listed in Mario F Triola textbook). Is body temperature basically the same at both times?

8:00 AM 97.0 96.2 97.6 96.4 97.8 99.2

12:00 AM 98.0 98.6 98.8 98.0 98.6 97.6

5. Handle missing data for the following data set using a) mean and b) median imputation based on:

i. Overall observation

ii. Id

iii. Group

iv. treatment