Stats midterm exam latest--The following table displays descriptive statistics on the participants involved in a study.

The following table displays descriptive statistics on the participants involved in a study.

Characteristic	Experimental Medication (n=100)	Placebo (n=100)
Mean (SD) Age, years	47.2 (4.3)	46.1 (5.1)
% Males	46%	58%
Mean (SD) Educational Level, years	13.1 (2.9)	14.2 (3.1)
Mean (SD) Annual Income, $000s	$36.560 ($1,054)	$37.470 ($998)
Mean Body Mass Index	24.7 (2.7)	25.1 (2.4)

1. Generate a 95% confidence interval for the mean age among participants assigned to the placebo.
2. Generate a 95% confidence interval for the difference in mean ages in participants assigned to the experimental versus the placebo groups.
3. Generate a 95% confidence interval for the difference in mean body mass index in participants assigned to the experimental versus the placebo groups.

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Question 210 pts

A clinical trial is run to assess the efficacy of a new pacemaker device in patients with atrial fibrillation (AF).  Two hundred participants are randomized to receive the new pacemaker or a currently available pacemaker.  There are two primary outcomes of interest – the number of days in a three-month period with an atrial fibrillation event and hospitalization for atrial fibrillation over the three month follow-up period.  Data on baseline characteristics and the outcomes are shown below.

Baseline Characteristics	New Pacemaker (n=100)	Available Pacemaker (n=100)
Mean (SD) Age, years	67.3 (5.9)	66.9 (5.6)
% Male	48%	52%
Outcomes
Mean (SD) Number of days with AF event	8.4 (3.2)	14.9 (3.9)
% Hospitalized for AF	4%	9%

1. Compute a 95% confidence interval for the difference in mean number of days with an AF event between participants receiving the new pacemaker as compared to the available pacemaker.
2. Compute a 95% confidence interval for the mean number of days with an AF event among participants receiving the new pacemaker.

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Question 310 pts

The following table shows the numbers of patients classified as underweight, normal weight, overweight and obese according to their diabetes status. 

	Underweight	Normal Weight	Overweight	Obese
Diabetes	8	34	43	65
No Diabetes	12	85	40	93

If a patient is selected at random,

1. What is the probability that they are overweight?                             
2. What is the probability that they are obese and diabetic?                 
3. What proportion of the diabetics are obese?                                     
4. What proportion of normal weight patients are not diabetic?           
5. What proportion of patients are normal weight or underweight?    

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Question 410 pts

An investigator wants to test whether exposure to second-hand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age).  Give two possible study designs and indicate the pros and cons of each.  Then, provide your recommendation for the most efficient design.

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Question 510 pts

A study is run to estimate the incidence of atrial fibrillation (AF) in men and women over the age of 60.  Development of atrial fibrillation was monitored over a 10 year follow-up period.  The data are summarized below.

	Developed AF	Did not Develop AF
Men	120	6453
Women	86	7074

1. Compute the cumulative incidence of AF in men and in women
2. Compute the relative risk of AF incidence comparing men to women
3. Compute the odds ratio of AF incidence comparing men and women

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Question 610 pts

The following data were collected in a survey of 8th graders and summarize their cell phone status.

	No cell phone	Conventional cell phone user	Smart phone user
Boys	22	60	45
Girls	34	88	27

1. What proportion of the 8th graders have cell phones?
2. What proportion of the boys do not have cell phones?
3. Is  ownership of a cell phone independent of sex?  Justify your answer.
4. What proportion of smart phone users are boys?  

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Question 710 pts

The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery. 

	Side effects present	Side effects absent
Screen positive	20	4
Screen negative	105	250

1. Compute the sensitivity of the test  
2. Compute the specificity of the test
3. Compute the false positive fraction
4. Compute the false negative fraction

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Question 810 pts

A random sample of eight adults aged 30 years were asked how much they spent on medical costs in the year 2009.  The following data were measured.

300      140      5600    520      470      700      640      1200

1. Compute the sample mean
2. Compute the sample standard deviation
3. Compute the sample median
4. Compute the first and third quartiles

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Question 910 pts

Four hundred melanoma patients were diagnosed according to the type of skin cancer and the location of the skin cancer.  This data is presented below.

	Location
Type	Head and Neck	Trunk	Extremities	Total
Hutchinson’s Melanomic Freckle	22	2	10	34
Indeterminate	11	17	28	56
Nodular	19	33	73	125
Superficial Spreading Melanoma	16	54	115	185
Total	68	106	226	400

1.  What proportion of patients had Superficial Spreading Melanoma?  
2. Of patients with a skin cancer on the Trunk, what proportion had a nodular skin cancer? 
3. What proportion of patients had a Hutchinson’s Melanomic Freckle on the extremities? 
4.  Is type of skin cancer independent of location?  Justify your answer.

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Question 1010 pts

The gestation period for human births can be taken as normally distributed with a mean of 266 days and a standard deviation of 16 days.

1. What is the probability that a randomly chosen baby had a gestation period of more than 280 days?
2. If a gestation period if 276 days, what percentile among human births is this?