Chapter 8: Q2E (page 458)
What are the treatments for a designed experiment with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?
There are ten treatments (A,50), (A,60), (A,70), (A,80), (A,90), (B,50), (B,60), (B,70), (B,80), (B,90).
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Question: Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 6.29 (p. 348). Recall that the variable of interest was the average distance separating traps—called trap-spacing—deployed by teams of fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap-spacing measurements for eight teams from the Punta Abreojos (PA) fishing cooperative are listed. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives.
BT Cooperative | 93 | 99 | 105 | 94 | 82 | 70 | 86 | |
PA Cooperative | 118 | 94 | 106 | 72 | 90 | 66 | 98 |
Source: Based on G. G. Chester, “Explaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,” Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1).
a. Identify the target parameter for this study.b. Compute a point estimate of the target parameter.c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?d. Find aconfidence interval for the target parameter.e. Use the interval, part d, to make a statement about the difference in mean trap-spacing measurements of the two fishing cooperatives.f. What conditions must be satisfied for the inference, part e, to be valid?
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (December 2007) study of honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample were randomly divided into groups. One group received a dosage of an over-the-counter cough medicine (DM); another group received a dosage of honey (H). The coughing improvement scores (as determined by the children’s parents) for the patients in the two groups are reproduced in the accompanying table. The pediatric researchers desire information on the variation in coughing improvement scores for each of the two groups.
a. Find a 90% confidence interval for the standard deviation in improvement scores for the honey dosage group.
b. Repeat part a for the DM dosage group.
c. Based on the results, parts a and b, what conclusions can the pediatric researchers draw about which group has the smaller variation in improvement scores? (We demonstrate a more statistically valid method for comparing variances in Chapter 8.)
Honey Dosage | 11 12 15 11 10 13 10 13 10 4 15 16 9 14 10 6 10 11 12 12 8 12 9 11 15 10 15 9 13 8 12 10 9 5 12 |
DM Dosage | 4 6 9 4 7 7 7 9 12 10 11 6 3 4 9 12 7 6 8 12 12 4 12 13 7 10 13 9 4 4 10 15 9 |
It is desired to test H0: m = 75 against Ha: m 6 75 using a = .10. The population in question is uniformly distributed with standard deviation 15. A random sample of size 49 will be drawn from the population.
a. Describe the (approximate) sampling distribution of x under the assumption that H0 is true.
b. Describe the (approximate) sampling distribution of x under the assumption that the population mean is 70.
c. If m were really equal to 70, what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
d. What is the power of this test for detecting the alternative Ha: m = 70?
Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy x of a professional soccer player’s shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target,x=0; if he misses his target 2 feet to the right, x=2; and if he misses 1 foot to the left,x=-1.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where he is standing; all other shots on goal will score. Consider a goalkeeper who stands in the middle of the goal.
a. If the player aims for the right goalpost, what is the probability that he will score?
b. If the player aims for the center of the goal, what is the probability that he will score?
c. If the player aims for halfway between the right goal post and the outer limit of the goalkeeper’s reach, what is the probability that he will score?
Question: Refer to the Journal of Business Logistics (Vol. 36, 2015) study of the factors that lead to successful performance-based logistics projects, Exercise 2.45 (p. 95). Recall that the opinions of a sample of Department of Defense (DOD) employees and suppliers were solicited during interviews. Data on years of experience for the 6 commercial suppliers interviewed and the 11 government employees interviewed are listed in the accompanying table. Assume these samples were randomly and independently selected from the populations of DOD employees and commercial suppliers. Consider the following claim: “On average, commercial suppliers of the DOD have less experience than government employees.”
a. Give the null and alternative hypotheses for testing the claim.
b. An XLSTAT printout giving the test results is shown at the bottom of the page. Find and interpret the p-value of the test user.
c. What assumptions about the data are required for the inference, part b, to be valid? Check these assumptions graphically using the data in the PBL file.
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