An experiment studied the efficacy of using 95% ethanol or 20% bleach as a disin

Question

An experiment studied the efficacy of using 95% ethanol or 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25°C for 4 weeks. The observation reported was the number of uncontaminated eggplant cuttings after the 4-week storage.

(a) Are you willing to assume that the underlying variances are equal?

YesNo    

(b) Using the information from part (a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested? (Use 1 for 95% ethanol disinfectant and 2 for 20% bleach disinfectant. Use = 0.05. Round your answer to three decimal places.)

1-2. Null and alternative hypotheses:

H0: 1 2 0 versus Ha: 1 2 = 0H0: 1 2 < 0 versus Ha: 1 2 > 0    H0: 1 2 = 0 versus Ha: 1 2 < 0H0: 1 2 = 0 versus Ha: 1 2 > 0H0: 1 2 = 0 versus Ha: 1 2 0

3. Test statistic:  t =  

4. p-value:

p-value < 0.0100.010 < p-value < 0.020    0.020 < p-value < 0.0500.050 < p-value < 0.1000.100 < p-value < 0.200p-value > 0.200

5. Conclusion:H0 is rejected. There is insufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.H0 is not rejected. There is insufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.    H0 is rejected. There is sufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.H0 is not rejected. There is sufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.

Disinfectant 95% Ethanol     20% Bleach Mean   3.78   4.80 Variance   2.78096   0.17145 n 15 15 Pooled variance 1.47621

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(with pooled variances)

Hypothesis test results:

Hence,

a) Yes

1 - 2. H0: 1 2 = 0 versus Ha: 1 2 0

3. t = -2.3565

4. 0.020 < p-value < 0.050

5. H0 is rejected. There is sufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -1.02 0.43284756 28 -2.3564878 0.0257

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