Home / Questions / For the theory section show your work and do not round off your middle work Keep your fina...
For the theory section, show your work and do not round off your middle work.
Keep your final answer to four (4) decimal places, where relevant.
1. To compare whether the mean level of saturated fat is different in three different brands of margarine (A, B and C), a researcher took five (5) samples each of the three different brands and analysed the level of fat. The result given below is the fat content (in grams) in a 20-gram serving:
Brand A Brand B Brand C
12.5 15.3 14.2
13.2 15.4 13.9
12.8 14.6 14.3
13.0 15.0 14.5
12.9 14.5 13.8
a. Use Hartley’s F test and verify whether the condition about variance is satisfied.
b. Can it be concluded at the 5% significance level that there are differences in the mean level of saturated fat between the three brands. [Assume that all requirements are satisfied for this test.]
c. What happens to the F statistic when the sample size increases; for example, from 5 to 15. Justify your answer.
2. In an experiment with t = 5; and n1 = 5; n2 = 7; n3 = 3; n4 = 8; n5 = 7 — suppose we define the following contrasts:
C1 = y1 + y2+ 2y3 - 3y4 - y5
C2 = y1 + y2 - 2y4
a. Are these contrasts linear? Justify your answer.
b. Are these contrasts orthogonal? Justify your answer.
3. What is a Type I error? Distinguish between experiment-wise Type I error rate and comparison-wise Type I error rate. Which of these error rates is often controlled by researchers via use of methods such as the Bonferonni adjustment and why?
4. In a research study involving eight (8) treatments, five contrasts were selected by the researcher for comparing various hypotheses about the treatment means.
a. If we want to control the experiment-wise error rate at a level of alphaE = 0.05, using the Bonferroni inequality, what value should be selected for alphaI.
b. What is the critical value from the F table for testing the five contrasts if the sample size is 6 for each of the 8 samples.
5. A study was conducted to compare five different types of candies. The variable of interest was the “taste value.” A group of 300 people were asked to rate the taste from 1 (poor) to 4 (excellent), after tasting the candies. The candy types were
Type A: Chewy from Expensive Brand 1
Type B: Crunchy from Expensive Brand 1
Type C: Chewy from Inexpensive Brand 2
Type D: Crunchy from Inexpensive Brand 2
Type E: Crunchy from Expensive Brand 3
The mean ratings for the five types are given below:
Type A B C D E
Mean Rating 2.32 2.56 3.22 2.94 3.76
The mean square error is 0.2457.
a. Consider a contrast of {-2, -2, 3, 3, -2}. Please explain in words which combination of the 5 types of candy in this study is being compared with which other combination of the 5 types of candy in this study by this contrast. (Hint: Striving to understand the 4 contrasts and their associated a1, a2, a3, a4, and a5 values shown in Table 9.3 on page 111 in the textbook might prove helpful to you with answering this question.)
b. What is this value of the contrast?
c. What is the sum of squares for this contrast?
d. Is there significant evidence that the mean value of the contrast is not zero?
6. a. Use Fisher’s LSD method with alpha = 0.05 to determine which population means differ in the following problem:
t = 3; MSE = 800
Sample size 20 20 20
Sample mean
130 100 140
b. Repeat the experiment using the Bonferroni adjustment.
c. Use Tukey’s multiple comparison method to see which population means differ in the given problem.
7. Consider the following treatment means from an experiment with seven (7) observations per treatment. The MS error = 0.8. Use Scheffe’s method for testing the significance of the contrasts with coefficients {-3, -1, +2, +1, +1}. Use 0.05 as the level of significance.
Treatment A B C D E
Mean 3.0 2.0 2.5 1.5 4.5
8. An experiment was conducted with 5 treatments and 4 observations per treatment. Treatment A was the control. The treatment means and the means square error are shown below. Which if the other treatments are significantly less that the control at the 5% level of significance.
Treatment A B C D E
Mean 70 80 60 90 85
MSE = 20.
Apr 02 2020 View more View Less
Suppose rRF = 3%, rM = 9%, and rA = 15%. Calculate Stock A's beta. Round your answer to two decimal places. If Stock A's beta were 2.0, then what would be A's new require...
Jul 16 2021Boulder Mountain Ski Company has total assets of $472,800,000 and a debt ratio of 025 Calculate the companyâ€™s debt-to-equity ratio
Mar 22 2020Sales during the year were 500 units. Beginning inventory was 200 units at a cost of $5 per unit. Purchase 1 was 250 units at $6 per unit. Purchase 2 was 400 units at $7 ...
Mar 29 2020Altruistic Company has an outstanding financial performance year, which generates excess cash of $2,000,000, which it chooses to purchase the following financial instrume...
Jul 25 2021Calculate the initial investment associated with each of Clark Upholstery’s alternatives. b. Calculate the incremental operating cash inflows associated with each of Clar...
May 28 2020By using the same alkene, how do you synthesize the following alcohols? Give the alkene and show the mechanisms for each product formation. ОН. НО. X " ОН
May 17 2021the Australian Dangerous Goods Code outlines configurations for Dangerous Goods placards (i.e. where to place the placards - front, back side etc.). explain the configura...
Apr 22 2021Changes in the money supplyThe following graph represents the money market in a hypothetical economy. As in the United States, this economy has a central bank called the ...
Jul 03 2021what are compounds composed of?
Jun 28 2021If an identical product can be sold in two different markets, and no restrictions exist on the sale or transportation costs, the product's price should be the same in b...
Apr 18 2021