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 four weeks. The observation reported was the number of uncontaminated eggplant cuttings after the four-week storage.

Disinfectant	95% Ethanol	20% Bleach
Mean	3.76	4.84
Variance	2.78099	0.17149
n	15	15
Pooled variance 1.47624

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

Yes

No    

(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 μ₁ for 95% ethanol disinfectant and μ₂ for 20% bleach disinfectant. Use α = 0.05.)

State the null and alternative hypotheses.

H₀: (μ₁ − μ₂) < 0 versus H_a: (μ₁ − μ₂) > 0

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) ≠ 0    

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) > 0

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) < 0

H₀: (μ₁ − μ₂) ≠ 0 versus H_a: (μ₁ − μ₂) = 0

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

State the p-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.

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 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 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.

Answer 1

a) Yes. Because the pooled variance value is already given in the data, so we can assume that the population variances are equal.

b) H0:

    Ha:

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                            = (3.76 - 4.84)/sqrt(1.47624/15 + 1.47624/15)

                            = -2.434

DF = 15 + 15 - 2 = 28

P-value = 2 * P(T < -2.434)

            = 2 * 0.0108

            = 0.0216

0.020 < P-value < 0.050

Since the P-value < (0.0216 < 0.05), so we should reject the null hypothesis.

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.