Discuss the below:
Q1. A sample of the reading scores of 25 sixth-graders has a mean of 82, and the standard deviation of the sample is 15. Assume that the population can be adequately approximated by a normal distribution.
(a) Find the 95% confidence interval of the mean reading scores of all sixth-graders.
(b) Find the 85% confidence interval of the mean reading scores of all six-graders
Q2. The times (in minutes) it took six white mice to learn to run a simple maze and the times it took six brown mice to learn to run the same maze are given here.
White Mice Brown Mice
18 25
24 16
20 19
13 14
15 16
12 10
(a) Does the color of the mice make a difference in their learning rate? Test using a significance level of 5%.
(b) Give the p-value for the test, and interpret this value.
(c) Find the 99% confidence interval for the difference of the means. Interpret this interval.
Note: You can assume that the data is normally distributed.
Q3. Three different relaxation techniques are given to randomly selected patients in an effort to reduce their stress levels. A special instrument has been designed to measure the percentage of stress reduction in each person. The data is shown below. You can assume normality and that good randomization and experimental procedures were used.
Relaxation Experiment
Technique I Technique II Technique III
3 12 15
10 12 14
5 17 18
1 13 14
13 18 20
3 9 22
4 14 16
Carry out a "complete" analysis using ANOVA and a 5% significance level.
Q4. A researcher wishes to determine if the number of hours (Y) a person exercises per week is related to their age (X). The data is shown below, and you can assume a well designed experiment was used to obtain the data.
Age (X): 18 22 26 32 35 38 52 59
Hours (Y): 10 8 5 2 4 3 1.5 1
Carry out a "complete" analysis using Simple Linear Regression and a 5% significance level. In addition, use your results to estimate the average amount of exercise for a 29 year old person, and provide a 98% C.I. for your estimate. Remember in your analysis to discuss the pertinent results obtained.
Q5. (a) A researcher surveyed married women and single women to ascertain whether there was a difference in the number of books each had read during the past year. The data is shown below.
Books Read
Married Single
6 2
8 3
7 5
4 11
9 3
12 5
13 11
7 12
10 16
18 4
15 0
1
You can't assume normality, so use an appropriate nonparametric method to Test the claim that each group read the same number of books. Test using a significance level of 10%. Draw appropriate conclusions.
(b) You are curious what the result would be if you used a parametric technique, so please re-do the analysis using the appropriate two sample t-test.
Q6. An experiment was conducted to study the effects of temperature of freezer (X1) and freezer storage density (X2) on number of days before flavor deterioration (Y) occurs, for a food product stored in a commercial freezer. The independent variables are measured in terms of deviations from the levels normally used; thus in the first observation the temperature setting was 10 degrees centigrade below the normal setting and the storage setting was 10 percentage points less than the normal density. Note: This coding should not concern you, and has nothing to do with carrying out the regression. The results of the study are as follows:
Y: 196 169 138 179 158 122 164 139 108
X1: -10 0 +10 -10 0 +10 -10 0 +10
X2: -10 -10 -10 0 0 0 +10 +10 +10
The following model is proposed:
Y = b0 + b1x1 + b2x2 + e
Carry out a "complete" multiple regression analysis of this model. In addition predict y for x1 = -5, and x2 = 5, and give a 95% C.I. for both Y|X, and E[Y|X].