Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms….

Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped air from the room over a Petri dish at the rate of 1 cubic foot per hour. Colonies of bacteria were allowed to form in the Petri dishes. The results are presented in the table below. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers.

n Mean bacteria per square foot Standard Deviation (Bacteria per square foot)
Carpeted (µ1µ1) 8 11.2 2.68
Uncarpeted (µ2µ2) 8 9.79 3.21

The question researchers want to answer is: Do carpeted rooms have more bacteria than uncarpeted rooms?

(You may not need all of the following symbols, but please type “mu1” for µ1, “mu2” for µ2, “sigma” for s ,“neq” for ??, and don’t include extraneous spaces).

a. State the null hypothesis.

b. State the alternative hypothesis.

c. What p-value do you get when you perform the appropriate hypothesis test? Round your answer to 3 decimal places.

d. Should the null hypothesis be rejected at the a=.05a=.05

level of significance? Type “reject” or “do not reject”.

e. Write a proper conclusion. (This question will be graded separately by the instructor, and will likely be marked incorrect by Canvas).

There is (type “sufficient” or “insufficient”) evidence at the a=.05a=.05 level of significance to conclude that carpeted rooms, .

f. What would it mean for the researcher to make a Type II error? (This question will be graded separately by the instructor, and will likely be marked incorrect by Canvas).

The researcher would conclude that carpeted rooms

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