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# Hypothesis test

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Here are some things I need help with:

? ALWAYS write out the NULL & HYPO (they come as a set) even if
the assignment does not ask you to do so
? Even though you write hypotheses using mathematical notations,
it is important to also get in the habit of writing them in words too...
things do get more complicated
? Always state the decision rule:
o The NULL hypothesis is NOT rejected because (fill in the blank)
therefore there is no support for the HYPOTHESIS that (copy & paste your
hypothesis here)
o The NULL hypothesis is rejected because (fill in the blank)
therefore there is support for the HYPOTHESIS that (copy & paste your
hypothesis here)
? TAILS: this concept is a big deal. You can understand
?
MEAN TO A MANAGER??" It will be good practice for later assignments

Problem 9.23 The data on the file CONCRETE1.xls represent the compressive strength in thousands of pounds per square inch (psi) of 40 samples of concrete taken two and seven days after pouring. (NOTE: the data is on the CD and is named CONCRETE1.XLS...it is also in the table below)
Sample Two days Seven days Sample Two days Seven days
1 2.83 3.505 21 1.635 2.275
2 3.295 3.43 22 2.27 3.91
3 2.71 3.67 23 2.895 2.915
4 2.855 3.355 24 2.845 4.53
5 2.98 3.985 25 2.205 2.28
6 3.065 3.63 26 3.59 3.915
7 3.765 4.57 27 3.08 3.14
8 3.265 3.7 28 3.335 3.58
9 3.17 3.66 29 3.8 4.07
10 2.895 3.25 30 2.68 3.805
11 2.63 2.85 31 3.76 4.13
12 2.83 3.34 32 3.605 3.72
13 2.935 3.63 33 2.005 2.69
14 3.115 3.675 34 2.495 3.23
15 2.985 3.475 35 3.205 3.59
16 3.135 3.605 36 2.06 2.945
17 2.75 3.25 37 3.425 4.03
18 3.205 3.54 38 3.315 3.685
19 3 4.005 39 3.825 4.175
20 3.035 3.595 40 3.16 3.43

a. At the .01 level of significance, is there evidence that the average strength is less at two days than at seven days?

b. What assumption is necessary to perform this test?

c. Find the p-value and interpret its meaning.

Problem 9.25 A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, "Do you enjoy shopping for clothing?" Of the 240 males, 136 answered yes and of the 260 females, 224 answered yes.
a. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing, at the .01 level of significance?

b. Find the p-value and interpret its meaning.

c. Set up a 99% confidence interval estimate of the difference between the proportion of males and females who enjoy shopping for clothing.

d. Compare the results of A & C.

e. What would be your answer to A-C if 206 males enjoyed shopping for clothing?

Problem 9.43 The director of training for a company manufacturing electronic equipment is interested in determining whether different training methods have an effect on the productivity of assembly-line employees. She randomly assigns 42 recently hired employees to two groups of 21. The first group receives a computer-assisted, individual-based training program, and the others receives a team-based training program. Upon completion of the training, the employees are evaluated on the time (in seconds) it takes to assemble a part. The results are as follows: (NOTE: the data is on the CD and is named TRAINING.XLS and below)
COMPUTER-ASSISTED, INDIVIDUAL-BASED TRAINING PROGRAM TEAM-BASED TRAINING PROGRAM
19.4 17.7 16.5 22.4 17.1 23.7
16.7 16.1 17.7 13.8 18 17.4
20.7 19.8 16.2 18.7 28.2 23.2
19.3 16.8 17.4 18 21.7 20.1
21.8 19.3 16.4 19.3 20.8 12.3
16.8 14.7 16.8 20.8 30.7 15.2
14.1 16 18.5 15.6 24.7 16

a. Using a .05 significance level, is there evidence of a difference between the variables in assembly times (in seconds) of employees trained in a computer-assisted, individual-based training program and those trained in a team-based program? HINT: we just studied a specific type of test.

b. On the basis of the results obtained in (a), is it appropriate to use the pooled-variance t test to compare the means of the two groups? Discuss.

Problem 9.53 The pet-drug market is growing very rapidly. Before new pet drugs can be introduced into the marketplace, they must be approved by the U.S. Food & Drug Administration (FD). In 1999, the Novartis company was trying to get Anafranil, a drug to reduce dog anxiety, approved. According to an article (Elyse Tanouye, "The Ow in Bowwow: With Growing Market in Pet Drugs, Makers Revamp Clinical Trials." Wall Street Journal, April 13, 1999), Novartis had to find a way to translate a dog's anxiety symptoms into numbers that could be used to prove to the FDA that that the drug had a statistically significant effect on the condition. (PHSTAT not needed for this problem)

a. What is meant by the phrase "statistically significant effect?"

b. Consider an experiment where dogs suffering from anxiety are divided into two groups. One group will be given Anafranil, and the other will be given a placebo (a drug without active ingredients). How can a dog's anxiety symptoms be translated into numbers? In other words, does a continuous random variable (X1), the measurement of effectiveness of the drug Ananfranil, and X2, the measurement of effectiveness of the placebo.

c. Building on your answer to part (b), define the null & hypothesis for the study.