Assignment 3 (Chapter 10 and 11)
Solve the following problems manually:
1. The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes.
Participant BMI (kg/m2)
A) Assuming the participants can be considered to be normally distributed, and that they come from a population with a σ=2.4 kg/m2, calculate a 95% confidence interval for the mean BMI of the population for which they represent.
B) Correctly interpret the confidence interval you found above.
2. A researcher is interested in the decrease in adolescent BMI after a new after school program is implemented to promote exercise in children. Suppose the researcher wants to collect a SRS of children from the program in order to evaluate their loss in BMI. If the population standard deviation is 4.87 kg/m2, and the researcher wants to capture the mean BMI within 4 kg/m2, how many children should he sample to attain 95% confidence?
3. A geographic researcher is interested in the variable describing average distance traveled to the nearest health center in a community and its association with a number of negative health outcomes. Suppose after a SRS of 416 households, the researcher calculates a sample average distance of 16.2 miles. Assume that the population standard deviation is 2.4 miles.
A) Construct a 99% confidence interval for the estimate.
B) Interpret the interval.
4. A new vitamin supplementation program is intended to decrease average resting heart rate in individuals at risk for hypertension. Assume that a team of researchers are hopeful that resting heart rate in their population will get down to less than 68 bpm, in a population with a standard deviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273 participants in their program and calculates a sample average resting heart rate of 74 bpm.
A) Carry out a one sample Z test to determine if the team can conclude that the supplementation program is successful in meeting their goal reduction in resting heart rate. Use an α=0.05.
B) Construct a 95% Confidence interval about the sample mean, and interpret the result.
5. A researcher is interested in the effectiveness of a new program at reducing the average systolic blood pressure in a population with a new anti-hypertensive medication. The researcher wants to test the hypothesis that the mean difference in systolic blood pressure is greater than 40 mmHG.
Which of the following represents the correct null and alternative hypotheses for the study?
A) Ho: µ1 – µ2 = 0, Ha: µ1 – µ2 = 40
B) Ho: µ1 – µ2 = 40 Ha: µ1 – µ2 ≠ 40
C) Ho: µD = 40 Ha: µD >40
D) Ho: µD = 40 Ha: µD ≠40
6. Researchers are interested in the effectiveness of a new therapeutic methodology at decreasing performance on the Global Depression Scale (GDS). Suppose clinical relevancy in this field would mandate that the methodology needs to decrease a score on the GDS in a clinically depressed individual by more than points. Which of the following represents the correct null and alternative hypotheses for the t test that should be implemented in this investigation?
A) Ho: µD=0, Ha: µD≠0
B) Ho: µD=5, Ha: µD≠5
C) Ho: µD=5, Ha: µD≤5
D) Ho: µD=5, Ha: µD>5
7. Suppose a researcher is interested in the effect of a new treatment drug at increasing CD4 count in patients with HIV. In this study, each patient treated with the study drug is frequency paired with another patient on a number of characteristics treated with a placebo to insure independence among samples. Assume the following sample of participants enrolled in the study represents an appropriate approximation to the normal distribution.
A 347 A’ 326
B 346 B’ 321
C 338 C’ 314
D 334 D’ 316
E 342 E’ 309
A) What type of study is this?
B) Carry out a paired-sample t test to investigate the effectiveness at increasing CD4 count in immunocompromised patients. Write out the null and alternative hypotheses using an α=0.05, and correctly interpret your results.
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