Is there a difference in the amount of airborne bacteria between carpeted and un

Question

Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, seven rooms were carpeted and seven were left uncarpeted. The rooms are similar in size and function. After a suitable period, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries are provided:

Carpeted rooms: x=184 s= 22.0

Uncarpeted rooms: x=175 s=16.9

The researcher wants to investigate whether the presence of carpet is associated with either an increase or decrease in the mean bacterial concentration in air. The P-value for this test is (use Option 2 for the degrees of freedom):

A. There are outliers in these data, so we can't rely on the two-sample t test.

B. This test is unreliable because the populations we're sampling from are heavily skewed. C. There isn't much evidence to support a conclusion that the presence of carpet is associated with an increase or decrease in the mean bacterial concentration of air. D. There is fairly strong evidence to support a conclusion that the presence of carpet is associated with an increase or decrease in the mean bacterial concentration of air.

Explanation / Answer

Mu1 = 184

Mu2 = 175

Sd1 = 22

Sd1 = 16.9,

N1 = n2 = 7

T statistic = (mu1 – mu2)/ sqrt( s1^2/n1 + s2^2/n2)

Df = n1 +n2-2

This is for equal variances and hence no pooled degrees of freedom

t-statistic = (184-175)/(22^2/7+16.9^2/7) = 0.8583

p-value = t(0.8583,10) = 0.4075

since p-value > 0.05 donot reject H0 (the null hypothesis that the carpeted room bacteria levels is equal to non-carpeted room bacteria levels).

Answer C

There isn't much evidence to support a conclusion that the presence of carpet is associated with an increase or decrease in the mean bacterial concentration of air.

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