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 HYpothesis : H0 : There is no significant difference between carpeted and non carpeted rooms containing bacteria. carpete = non-carpet

Alternative Hypothesis : Ha : There is significant diffeence between carpeted and non - carpeted room in terms of bacteria level. carpete > non-carpet

Test Statistic :

t = (xcarpeted - xuncarpeted)/ sqrt(sp2(1/n1 + 1/n2 ) = (9.725 - 7.525)/sqrt ( 7.070/ (1/8 + 1/8) =1.6547

tcritical = 2.6244

P- value calculating for calculator for given test statistic = 0.060

State the appropriate conclusion.

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

Answer is option b. as we cant reject the null hypothesis.

t-Test: Two-Sample Assuming Equal Variances Carpeted Uncarpeted Mean 9.725 7.525 Variance 5.147857 8.993571429 Observations 8 8 Pooled Variance 7.070714 Hypothesized Mean Difference 0 df 14

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