Question

rooms contained more bacteria than uncarpeted the air from the Researchers wanted to determine if carpeted rooms. To determine the amount of bacteria in a room, researchers pumped room over a Petri dish at the rate of I cubic foot per minute for eight carpeted rooms eight uncarpeted 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. 2) and rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. Carpeted Rooms Uncarpeted Rooms (bacteria/cubic foot) (bacteria/cubic food) 11.8 8.2 7.1 13.0 10.8 10.1 4.6 14.0 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 Source: William G. Walter and Angie Stober. "Microbial Air Sampling in a Carpeted Hospital." Journal of Environmental Health, 30 (1968). Do carpeted rooms have more bacteria than uncarpeted rooms? (Points: 10) i a) State the null and alternative hypotheses in words. State the null and alternative hypotheses using the mathematical notation. ii. b) Provide the formula(s) for calculating the test statistic. (Points: 5) Use Microsoft Excel Data Analysis ToolPak to test whether carpeted rooms have more bacteria than uncarpeted rooms at the a 0.05 level of significance. Excel worksheet ply containing the test results with your answers. (Points: 15) c) Attach the Microsoft d) What is your final answer for the test statistic according to the Microsoft Excel worksheet ply containing the test results? (Points: 5) e) What is (are) the critical value(s) for this hypothesis test according to the Microsoft Excel worksheet ply containing the test results? If this is a one-tailed test, make sure you report one critical value. If this is a two-tailed test, make sure you report two critical values. (Points: 5) Does the sample evidence suggest that carpeted rooms have more bacteria than uncarpeted rooms? State the correct conclusion ("There is sufficient evidence at the a-0.05 significance level to support " or"There is NOT sufficient evidence at the α-0.05 significance level to support..."). Make sure you state the conclusion in terms of H (Points: 10) t)

Answer 1

a)

Null Hypothesis H₀ : Both carpeted and uncarpeted rooms does not have any difference in bacteria per cubic foot.

Alternative Hypothesis H₁ : carpeted rooms have more bacteria per cubic foot than uncarpeted rooms have.

H_{0 : $\mu_{1}= \mu_{2}$}

H_{1: $\mu_{1} > \mu_{2}$}

b)

test statistic t $t = \frac{\bar{X_{1}}-\bar{X_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

where $\bar_{X_{1}}$ = mean of sample 1

$\bar_{X_{2}}$ = mean of sample 2

s₁² = variance of sample 1

s₂² = variance of sample 2

n₁ = size of sample 1

n₂ = size of sample 2

We can assume sample 1 is bacteria counts in carpeted rooms, and sample 2 is bacteria counts in uncarpeted rooms.

c)

t-Test: Two-Sample Assuming Equal Variances
	Carpeted room	Uncarpeted room
Mean	11.2	9.7875
Variance	7.168571	10.30411
Observations	8	8
Pooled Variance	8.736339
Hypothesized Mean Difference	0
df	14
t Stat	0.955771
P(T<=t) one-tail	0.177701
t Critical one-tail	1.76131
P(T<=t) two-tail	0.355402
t Critical two-tail	2.144787

d) test statistic t = 0.9557

e) Test is a one tailed test, critical value for one tailed test = 1.7613

f) Since test statistic is less than critical value we fail to reject null hypothesis and conclude that there is not sufficient evidence t the alpha =0.05 to support the claim that carpeted rooms have more bacteria per cubic foot than uncarpeted rooms have.