Question

In: Statistics and Probability

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table...

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

Carpeted   Uncarpeted
10.8    10.5
   6 8.4
9.8    6.5
8 6.7
14.7 11.7
9.2    5.5
15.6 13.3
9.9 10.6

Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.01 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

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

A. H0: μ1=μ2 H1: μ1>μ2

B. H0: μ1=μ2 H1: μ1≠μ2

C. H0: μ1<μ2 H1: μ1>μ2

D. H0: μ1=μ2 H1: μ1<μ2

Solutions

Expert Solution

We want to whether carpeted rooms have more bacteria than uncarpeted rooms at α=0.01 level of significance.

We have given that Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

So we conduct two sample t test with pooled (equal variance) variance because there is no large difference in variances of the two groups.

Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

µ1 be a population mean of captured room and µ2 be a population mean of uncaptured room.

H0 : µ1 = µ2

H1 : µ1 > µ2

You will get the following output in Excel

t-Test: Two-Sample Assuming Equal Variances

Variable 1

Variable 2

Mean

10.5

9.15

Variance

10.39714286

7.794286

Observations

8

8

Pooled Variance

9.095714286

Hypothesized Mean Difference

0

df

14

t Stat

0.895252122

P(T<=t) one-tail

0.192893093

t Critical one-tail

2.624494068

P(T<=t) two-tail

0.385786186

t Critical two-tail

2.976842734

From the above output,

Test statistics = 0.895

Since this test is one sided.

P value = 0.1929

Since p value = 0.1929 > 0.01 therefore we failed to reject null hypothesis.

Conclusion: There is no sufficient evidence to claim than carpeted rooms have more bacteria than uncarpeted rooms at α=0.01 level of significance.


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