1. True story...My oldest son's bus stop has 6 students at it, including him. It turns out that the other 5 are all female. (As a 7th grader, this is torture, but I have a feeling his opinions on the matter will change.) Assuming that the probability of male and female are both ½ in our school district, what is the probability of a child ending up with a bus stop as gender-unbalanced as my son's in our school district?
2. You are testing the claim that the standard deviation of wait times for an emergency room bed has grown past the previous standard deviation of 10.0 minutes. You take 50 sample data points and find the wait time average of 40.0 minutes and standard deviation 10.3 minutes. The data are approximately normally distributed. Perform a full hypothesis test to test the claim.
3. Your plant manager wants to determine the effect of ice cream flavor run on changeover time between batches for the three different changeovers that your plant does. You collect the following data. Is there a difference in changeover times based on the flavors? Perform a full hypothesis test at the 0.05 level and state your conclusion.
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Chocolate to strawberry
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Strawberry to vanilla
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Vanilla to chocolate
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|
3.8
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3.8
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6.1
|
|
6.8
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4.5
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4.3
|
|
6.4
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4.8
|
6.8
|
|
6
|
4.9
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6.2
|
|
5.1
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4.3
|
5.8
|
|
6.4
|
4.9
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3.6
|
|
3.5
|
5.9
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4
|
|
4.1
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5.8
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3.6
|
4. A quality manager conducted a study to assess the impact of shift on employee errors during an assembly task. Total errors were counted for employees during the three shifts of morning, afternoon, and night. With an alpha of 0.05, test whether the shift and number of errors are independent and clearly state your conclusion.
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Errors
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Morning
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Afternoon
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Night
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0
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18
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16
|
14
|
|
1
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10
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12
|
14
|
|
2
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4
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10
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14
|
|
3
|
7
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6
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4
|
5. Suppose you want to test the claim that the mean time to complete a set of multiplication facts differs between male and female 4th grade students. A simple random sample of 50 male students is taken and they complete the facts with a mean of 55 seconds and a standard deviation of 10.0 seconds. A simple random sample of 50 female students is also taken, and they complete the facts with a mean of 53.5 seconds and a standard deviation of 8.0 seconds. Using an alpha of 0.05, perform the hypothesis test and state your conclusion clearly.