An experiment was conducted to study the use of 95% ethanol versus 20% bleach as a disinfectant in removing contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using cuttings of eggplant tissue. The observation reported was the number of uncontaminated eggplant cuttings after a 4-week storage.

Disinfectant95% Ethanol20% BleachMean3.724.84Variance2.780910.17142n1515Pooled variance1.47617

(a)

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

Yes, the ratio of the larger variance to the smaller variance is less than three.

Yes, the ratio of the larger variance to the smaller variance is more than three.

No, the ratio of the larger variance to the smaller variance is less than three.

No, the ratio of the larger variance to the smaller variance is more than three.

It is not possible to check that assumption with the given information.

(b)

Using the information from part (a), is there evidence of a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested? (Use₁for 95% ethanol disinfectant and₂for 20% bleach disinfectant. Use= 0.05.)

State the null and alternative hypotheses.

H₀: (₁₂) = 0 versusH_a: (₁₂) > 0

H₀: (₁₂) < 0 versusH_a: (₁₂) > 0

H₀: (₁₂) = 0 versusH_a: (₁₂)0

H₀: (₁₂)0 versusH_a: (₁₂) = 0

H₀: (₁₂) = 0 versusH_a: (₁₂) < 0

State the test statistic. (Round your answer to three decimal places.)

t=

State thep-value.

p-value < 0.010

0.010 <p-value < 0.020

0.020 <p-value < 0.050

0.050 <p-value < 0.100

0.100 <p-value < 0.200

p-value > 0.200

State the conclusion.

H₀is 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.

H₀is 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.

H₀is 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.

H₀is 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.

You may need to use the appropriateappendix tableto answer this question.