A researcher wanted to determine if carpeted or uncarpeted rooms contain more ba

Question

A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacterial. The table shows the results for the number of bacteria per cubic foot for both types of rooms. Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the a-0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

Carpeted 
7.9, 6.3, 11.5,
13, 9.2,10.3,
11.6, 8

Uncarpeted
4.3, 4.8, 7.8,
4.3, 12.3, 8.2,
10.9, 7.6

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Determine the P-value for this hypothesis test.
P-value = ? (round 3 decimals)

State the appropriate conclusion.
a) do not reject H0. There is significant evidence at the a=0.01 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms
b) do not reject H0. There is not significant evidence at the a=0.01 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms
c) Reject H0. There is not significant evidence at the a=0.01 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms

Explanation / Answer

Null hypothesisHo:mean(carpeted)=mean(uncarpeted)

Alternative Hypothesis:Ho:mean(carpeted)>mean(uncarpeted)

perform t test for diff in means

its a one tail test

used excel to calculate t stat and p

t=1.654

p=0.061

p>0.01

Decsion:

Fail to reject null hypothesis

Accept null hypothesis:

There is no sufficient evidence at 1% level of significance to support the claim

b) do not reject H0. There is not significant evidence at the a=0.01 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms

t-Test: Two-Sample Assuming Unequal Variances carpeted uncarpeted Mean 9.725 7.525 Variance 5.147857 8.993571 Observations 8 8 Hypothesized Mean Difference 0 df 13 t Stat 1.654707 P(T<=t) one-tail 0.060956 t Critical one-tail 2.650309 P(T<=t) two-tail 0.121913 t Critical two-tail 3.012276

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