A sample of 20 managers was taken, and they were asked whether or not they usually take work from home.
Question 1
A sample of 20 managers was taken, and they were asked whether or not they usually take work from home. The responses of these managers given below, where yes indicates they usually take work home and no means they do not
yes yes no no no yes no no no no
yes yes no yes yes no no no no yes
a. Find a 95% confidence interval for the percentage of all managers who take work from home. Interpret confidence interval.
b. How large sample is required if we want to be 95% confident that our estimate of p is within 0.02?
Solution:
Question 2
The following data are collected from pregnant women to compare the Plasma ascorbic acid level of smokers and non-smokers.
Table: Plasma ascorbic acid values
Non-smokers 0.97, 0.72, 1.00, 0.81, 0.62, 1.32, 1.14, 1.22, 0.90, 0.74, 0.88, 0.94
Smokers 0.88, 0.71, 0.98, 0.79, 1.01, 1.16, 0.78, 1.28
Test whether there is any difference between plasma ascorbic acid levels of smokers and non-smokers. Also find 95% confidence interval for the difference of two means.
Describe your findings. Use alpha=0.05
[Hint: use hypothesis, test statistics confidence interval etc.]
Solution:
Question 3
Five treatments for fever blisters, including a placebo, were randomly assigned to 30 patients, with 6 patients receiving each treatment. The data in the table below are the numbers of days from initial appearance of the blisters until healing is complete.
Placebo Treatment 1 Treatment 2 Treatment 3 Treatment 4
5 4 6 7 9
8 6 4 4 3
7 6 4 6 5
7 3 5 6 7
10 5 4 3 7
8 6 3 5 6
Based on the scenario above answer the following questions:
Identify the dependent variable.
Which statistical test is appropriate to use on these data?
Using 5% level, determine whether five treatments differ significantly with regards to healing fever blisters? Specify the hypotheses tested in this study.
Carry out the hypothesis test(s) for part c above. What is the appropriate conclusion for this test?
Indicate the test used to compare individual means if the null hypothesis is rejected.
Perform the appropriate test if necessary according to your response in part e above.
Solution
Question 4
A new drug is proposed to lower total cholesterol and a study is designed to evaluate the efficacy of the drug in lowering cholesterol. Fifteen patients agree to participate in the study and each is asked to take the new drug for 6 weeks. However, before starting the treatment, each patient’s total cholesterol level is measured. The initial measurement is a pre-treatment or baseline value. After taking the drug for 6 weeks, each patient’s total cholesterol level is measured again and the data are shown below.
Initial Cholesterol
Cholesterol at Week 6
215 205
190 156
230 190
220 180
214 201
240 227
210 197
193 173
210 204
230 217
180 142
260 262
210 297
190 184
200 193
Based on the scenario above, analyse the data with appropriate statistical methods and describe your findings in details (both descriptive and inferential). Use alpha=0.05
[Hint: while describing inferential use hypothesis, test statistics confidence interval etc.]
Question 5
A diabetic person is interested in determining how the amount of aerobic exercise impacts his blood sugar. When blood sugar reaches 170 mg/dl, he goes out for a run at a pace of 10 minutes per mile. On different days, he runs different distances and measures his blood sugar after completing his run. The preferred blood sugar level is in the range of 80 to120 mg/dl. Levels that are too low or too high are extremely dangerous. The data generated are given in the following table:
Distance (miles),x Blood sugar(mg/dl gram),y
2 136
2 146
2.5 131
2.5 125
3 120
3 116
3.5 104
3.5 95
4 85
4 94
4.5 83
4.5 75
Based on the scenario above, analyse the data with appropriate statistical methods and describe your findings in details. Use alpha=0.05 [note: use all the concepts learnt]
Solution:
Question 6
Suppose, the following results from a vaccine trial carried out during an epidemic.
Vaccine Status Recovery Death
Vaccinated 1562 42
Unvaccinated 383 94
Describe the contingency table
Analyze the data using appropriate statistical methods and describe your findings. Use alpha=0.05
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