Question

1. An investigator has developed a new fertilizer for a certain species of plant. They are interested in determining if the fertilizer has an effect on the height (inches) of the plants. They conduct an experiment where a random sample of 15 plants are given the fertilizer and 15 random plants are given water to serve as a control.

Fertilizer	Water
60.58	58.16
73.18	57.64
64.32	56.98
57.66	56.14
63.69	54.82
64.75	53.01
53.19	57.39
58.32	55.35
61.14	56.31
61.53	51.31
55.16	59.77
62.52	55.85
65.56	58.08
46.83	52.94
71.00	52.13

Significance level a = 0.05

Using Minitab,

a. Evaluate the normality assumption.

b. Test the hypothesis that the two population variances are equal.

c. Calculate the value of the test statistic for part b using the formula from class, does this match the value computed by Minitab?

d. Produce a 95% confidence interval for the difference in means.

e. Provide an interpretation of the confidence interval produces in part d.

f. Conduct a hypothesis test to examine the investigator's primary question of interest.

g. Now calculate the value of the test statistics for part f, does this match the value computed by Minitab.

Answer 1

Part a.

Using Minitab:

• Go to Start menu and then move to Basic Statistics.
• Click on Normality Test and then enter the variables on the respective columns.
• Click Ok. After clicking OK, Minitab generates the probability plot in a separate window.

Here we can notice that since the P value is greater than .05, we can assume the “Fertilizer” and “Water” data is normal.

Part b.

To check whether the variances of two populations of interest are statistically significant different, we use the test of equal variance.

Null Hypothesis (H₀): σ²₁ = σ²₂

Alternative Hypothesis (H_a): σ²₁ ≠ σ²₂

• Click Basic Statistics → 2 Variances.
• A new window named “Two-Sample Variance” pops up.
• Click in the blank box of “Samples” , enter respective samples as shown in below figure.

Click “Options” and select
“Use test and confidence intervals based on normal distribution”

Part c.

Calculations using Formual:

Test statistic for equal variance F=

  

value of the test statistic for part b using the formula is match the value computed by Minitab.

Part d.

Please post the other questions separately. As per our answering guidelines, we are supposed to answer just one question or four sub parts of the same question.
Hope this will be helpful. Thanks and God Bless You:) If any query in the solution, please post in comments