Question

Carpeted Uncarpeted

12.2   7.5
10.8   10.9
12.8   6.7
11.6   6.7
14.6   5.7
14.1   7.3
15.4   7.6
15   6.8
14.6   7
11.5   8.6
16.9   7.7
14.4   8.8
11.2   9.1
13.6   8.9
15.8   8.9
13.6   8.5
16.5   9.9
13.6   6.7

Problem 2: Appropriateness of Inference (again)

For the following scenario, answer the following questions. The underlined text is the name of the StatCrunch data set to be used for that part. Please note, do not conduct inference in this problem; just answer each question.

Bacteria Counts. 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 the rate of 1 cubic foot per minute for a random selection of eighteen carpeted rooms and another random sample of eighteen uncarpeted rooms in a very large hospital. Colonies of bacteria were allowed to form in the Petri dishes. The data are presented as the count of bacteria per cubic foot.

1. What is (are) the parameter(s) of interest? Choose one of the following symbols m (the population mean); m_D(the mean difference from paired (dependent) data);m₁ - m₂ (the difference of two independent means) and describe the parameter in context of this question in one sentence.

2. Depending on your answer to part (a), construct one or two relative frequency histograms. Remember to properly title and label the graph(s). Copy and paste these graphs into your document.

3. Describe the shape of the histogram(s) in one sentence.

4. Depending on your answer to part (a), construct one or two boxplots and copy and paste these graphs into your document.

5. Does the boxplot (or do the boxplots) show any outliers? Answer this question in one sentence and identify any outliers if they are present.

6. Considering your answers to parts (c) and (e), is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences.

Answer 1

a) The parameter of interest is m₁ - m₂ (the difference of two independent means). Where m1 and m2 are the means count of bacteria per cubic foot for Colonies of bacteria.

b) Depending on your answer to part (a), the two relative frequency histograms are

c) The shape of the histograms are symmetric.

d) Depending on your answer to part (a), two boxplots are:

e) The boxplots do not show any outliers.

f) Considering our answers to parts (c) and (e), it is appropriate inference in this case. Because the required two-sample t-test required normal distribution on both samples.