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Statistics Problem: Bacteria in Carpeted Rooms

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Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at a rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results were collected. A normal probability plot and box plot indicate the data are approximately normally distributed with no outliers. The data is as follows in bacteria per cubic foot:

Carpeted: 11.8, 10.8, 8.2, 10.1, 7.1, 14.6, 13.0, 14.0
Uncarpeted: 12.1, 12.0, 8.3, 11.1, 3.8, 10.1, 7.2, 13.7

Determine using the appropriate hypothesis testing technique if carpeted rooms have more bacteria than uncarpeted rooms at the .05 level of significance.

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Null Hypothesis: The mean amount of bacteria per cubic foot in carpeted rooms is lower than or equal to that in uncarpeted rooms. H0: u1 <= u2
Alternate Hypothesis: The mean amount of bacteria per cubic foot in carpeted rooms is greater than that in uncarpeted rooms. H1: u1 > u2

Since ...

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Accept that the coin is fair if in 30 tosses the coin gives between 11 and 19 heads (inclusive); reject the hypothesis of fairness otherwise.

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Plot the type I error probability and the power function of this particular test.

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Then, a 21st observation was collected and this new observation was 10. Recompute the t-statistic when all 21 observations are used.

Comment on what you find.

4. In 8 hospital rooms that are carpeted, and another 8 that are uncarpeted, bacteria per cubic ft. were counted, and the data are as follows:

Carpeted rooms: 11.8, 8.2, 7.1, 13, 10.8, 10.1, 14.6, 14
Uncarpeted rooms: 12.1, 8.3, 3.8, 7.2, 12, 11.1, 10.1, 13.7
Compute a nominal 90% confidence interval for the difference in mean bacterial count per cubic ft. in carpeted and uncarpeted hospital rooms. Discuss the pros and cons of each type of confidence interval for this particular application. Discuss what assumptions you would be concerned about and whether you can test them, if you have any doubts.

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