ISE 362 HOMEWORK THREE Due Date: Thursday 10/06
1. Researchers want to determine the effectiveness of various treatments on glucose levels of diabetic rats. They randomly assign diabetic albino rats into four treatment groups. Group 1 rats served as a control group and were fed a regular diet. Group 2 rats were served a regular diet supplemented with a herb, fenugreek. Group 3 rats were served a regular diet supplemented with garlic. Group 4 rats were served a regular diet supplemented with onion. The basis for the study is that Persian folklore states that diets supplemented with fenugreek, garlic, or onion help to treat diabetes. After 15 days of treatment, the blood glucose was measured in milligrams per deciliter (mg/dL). The results of the experiment are presented in the table below. The researcher wants to determine if there is a difference in the mean glucose among the four treatment groups. Test this claim at the α = 0.05 level of significance. Assume that the underlying probability distributions are normal and the population σ’s are equal.
Table Measurement (mg/dL) mean s
Control >288.1, 296.8, 267.8, 256.7, 292.1, 282.9, 260.3, 283.8> 278.56 15.03 Fenugreek > 229.1, 240.7, 239.4, 207.7, 225.7, 230.8, 206.6, 213.3> 224.16 13.49
Garlic > 177.4, 202.2, 163.1, 184.7, 197.9, 164.6, 193.9, 158.1> 180.24 17.06
Onion > 299.7, 258.3, 286.8, 244.0, 267.1, 297.1, 249.9, 265.1> 271.00 21.18
Parameters:
Null H0:
Ha:
Test Statistic:
Reject Region:
Cal:
Decision:
P-value (Estimate or Use Range):
2. In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 225-cc two-stroke motorcycle, five plugs of each brand were tested and the number of miles (at a constant speed) until failure was observed. The partial ANOVA table for the data is given below. Fill in the missing entries, state the relevant hypotheses, and carry out a test at the α = 0.10 level by obtaining as much information as you can about the P-value.
Source / Df / SS / MS / fBrand
Error / 14,700
Total / 310,200
Null H0:
Ha:
Decision:
3. Your medical supplies company uses four different laboratories to execute chemical analyses on FDA approved quality control trials. A study is designed to investigate the four laboratories to see if they give, on the average, the same results. Samples of the same material are sent to the four laboratories. The analytical results for the four laboratories are shown in the table on the next page. Your contribution to this review is to use Bartlett’s test to test the hypothesis that the population variances of the four laboratories are not significantly different at the α = 0.01 level. Measurements of this type can be shown to follow a normal distribution.
Laboratory: Measurements______Sample mean S______
A > 58.7 61.4 60.9 59.1 58.2 > 59.66 1.41
B > 62.7 64.5 63.1 59.2 60.3 > 61.96 2.16
C > 55.9 56.1 57.3 55.2 58.1 > 56.52 1.16
D > 60.7 60.3 60.9 61.4 62.3 > 61.12 0.77 Parameters:
Null H0:
Ha:
Test Statistic:
Reject Region:
Calculate:
Decision:
4. Consider the accompanying data on plant growth after the application of different types of growth hormone. Perform an F-test at the α = 0.05 level while filling in the ANOVA table.
1 / 15 / 19 / 9 / 162 / 23 / 15 / 22 / 19
Hormone / 3 / 20 / 17 / 22 / 19
4 / 9 / 13 / 20 / 12
5 / 8 / 13 / 17 / 10
Source / df / SS / MS / f
Treatments
Error
Total
Null H0:
Ha:
Decision:
5. Apply Tukey’s procedure to Problem #4.
6. Consider a single-factor ANOVA experiment in which I = 3, J = 5, Sample mean for X1 = 15, sample mean for X2 = 16, and the sample mean for X3 = 22. Find values for SSE for which ¦0 > F.05, 2, 12 so that Null H0: m1 = m2 = m3 is rejected, yet when Tukey’s procedure is applied none of the true means can be said to differ significantly from one another.
Ans:
7. Folacin is the only B vitamin present in any significant amount in tea. Recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea. Does the data suggest that the true mean folacin content is the same for all brands? Execute a test at the α = 0.05 level and make sure to fill in the ANOVA table with the proper values.
Brand Observations
1 / 8.0 / 6.3 / 6.7 / 8.7 / 9.0 / 10.2 / 9.72 / 5.8 / 7.6 / 9.9 / 6.2 / 8.5
3 / 6.9 / 7.6 / 5.1 / 7.5 / 5.4 / 6.2
4 / 6.5 / 7.2 / 8.0 / 4.6 / 5.1 / 4.1
Parameters of interest:
Null H0:
Ha:
Source / df / SS / MS / fTreatments
Error
Total
Decision:
8. For the four treatment groups in problem #1, find the sample size necessary for each treatment to provide a power of 0.99 to detect a value of å (mi – m)2 = 1,721 between the treatment means at the α = 0.01 level. Assume a valid estimate for the population standard deviation σ is s = √MSE = 16.936.
Ans:
THE END