Prepare a written response to the following questions:
1. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?
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Hypothesis Test: Independent Groups (t-test, pooled variance)
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Larry
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George
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4.77
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5.02
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mean
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1.05
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1.23
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std. dev.
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40
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50
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n
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88
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df
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-0.25000
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difference (Larry - George)
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1.33102
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pooled variance
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1.15370
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pooled std. dev.
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0.24474
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standard error of difference
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0
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hypothesized difference
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-1.02
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t
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.3098
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p-value (two-tailed)
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-0.73636
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confidence interval 95.% lower
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0.23636
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confidence interval 95.% upper
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0.48636
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margin of error
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2. A consumer organization wants to know if there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below.
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Discount toy
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Variety
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Department
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$12
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15
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19
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13
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17
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17
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14
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14
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16
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12
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18
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20
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15
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17
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19
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An ANOVA was run and the results are shown below. At the .05 significance level, is there a difference in the mean prices between the three stores? What is the p-value? Explain why an ANOVA was used to analyze this problem.
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One factor ANOVA
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Mean
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n
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Std. Dev
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13.2
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5
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1.30
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Discount Toys
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16.2
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5
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1.64
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Variety
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18.2
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5
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1.64
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Department
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15.9
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15
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2.56
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Total
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ANOVA table
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Source
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SS
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df
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MS
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F
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p-value
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Treatment
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63.33
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2
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31.667
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13.38
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.0009
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Error
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28.40
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12
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2.367
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Total
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91.73
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14
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3. A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets?
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Plan A
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Plan B
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Plan C
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5
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6
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7
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7
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7
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8
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4
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7
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9
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5
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5
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8
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4
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6
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9
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An ANOVA was run and the results are shown below. At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value? What can you do to determine exactly where the difference is?
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One factor ANOVA
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Mean
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n
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Std. Dev
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5.0
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5
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1.22
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Plan A
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6.2
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5
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0.84
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Plan B
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8.2
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5
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0.84
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Plan C
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6.5
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15
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1.64
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Total
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ANOVA table
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Source
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SS
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df
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MS
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F
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p-value
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Treatment
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26.13
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2
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13.067
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13.52
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.0008
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Error
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11.60
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12
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0.967
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Total
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37.73
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14
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