stats help!!!!!!!!!

1. Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for the population of children is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 60 children with chronic bronchitis is studied, and its mean PEF is 279 with a standard deviation of 85. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at ?=0.05. If the results of the test are statistically significant, you must indicate the p-value for the test statistic. This problem is worth 15 points.

2. Consider again the study in Problem 1. A different investigator conducts a second study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without. Data on PEF are collected and summarized in the following table. Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis (n=25) as compared to those without chronic bronchitis (n = 25). Run the appropriate test at ?=0.05. If the results of the test are statistically significant, you must indicate the p-value for the test statistic. This problem is worth 15 points.Note: M= mean; SD = standard deviation.

	Chronic Bronchitis	No Chronic Bronchitis
	M	SD	M	SD
PEF	281	68	319	74

3. A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at ? = 0.05. If the results of the test are statistically significant, you must indicate the p-value for the test statistic. This problem is worth 15 points.

Subject Number	Initial Weight (lbs)	Weight after 6 Weeks (lbs)
1	155	157
2	142	145
3	176	180
4	180	175
5	210	209
6	125	126

4. A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to placebo. Pregnant women are enrolled and randomly assigned to receive one of three treatments: the experimental drug, the standard drug, or the placebo. Women are followed through delivery and classified as either delivering preterm (< 37 weeks) or not. The data are shown in the following table.

	Experimental Drug	Standard Drug	Placebo
Preterm Delivery
Yes	26	30	36
No	83	74	60

Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at ? = 0.05. If the results of the test are statistically significant, you must indicate the p-value for the test statistic. This problem is worth 15 points.

5. In 2007, the CDC reported that approximately 6.6 per 1000 (0.66%) children were affected with autism spectrum disorder. A sample of 4000 children from Boston is tested, and 280 children from the sample are diagnosed with autism spectrum disorder. Is the proportion of children affected with autism spectrum disorder higher in Boston as compared to the national estimate? Run the appropriate test at ? = 0.05. If the results of the test are statistically significant, you must indicate the p-value for the test statistic. This problem is worth 15 points.

Exercise Group	n	M	SD
Weight Training	20	49.7	10.2
Aerobic Exercise	20	43.1	11.1
Stretching/Yoga	20	57.0	12.5

6. A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups - Weight training, Aerobic exercise or Stretching/Yoga – and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below. Note: M= mean; SD = standard deviation.

Is there a significant difference in mean HDL levels among the exercise groups? Run the test at ? = 0.05. HINT: SSerror = 7286.5. This problem is worth 15 points.

7. A clinical trial is being planned to investigate the effect of a new experimental drug designed to reduce total serum cholesterol. Investigators will enroll participants with total cholesterol levels between 200 and 240, they will be randomized to receive the new drug or a placebo and followed for 2 months, and the total cholesterol will be measured. Investigators plan to run a test of hypothesis at ? = 0.05 and want 80% power to detect a difference of 10 points in mean total cholesterol levels between groups. They assume that 10% of the participants randomized will be lost over the 2 month follow-up. How many participants must be enrolled in the study? Assume that the standard deviation of total cholesterol is 18.5. This problem is worth 10 points.