**IVE ATTACHED PICTURES OF THE QUESTION AND ALL THE INFORMATION NEEDED**I WILL RATE AND LEAVE FEEDBACK**

Question 1:

Suppose we want to test whether or not three population means are equal. We can assume the population variances are equal and there is only one factor of difference. We want to perform this test with a 1% significance level.

a) If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding aType I error)?_________.

Suppose we, instead, run three separate hypothesis tests (t-tests), each with 1% significance level.

• Mean 1 = Mean 2
• Mean 1 = Mean 3
• Mean 2 = Mean 3

b) What is the probability that all three tests would be accurate? Hint: useprinciples of probabilityto help with calculations: P(accurate AND accurate AND accurate)_____________(Write answer accurate without rounding.)

c) Why would we use ANOVA instead of three separate tests?

d) Why would we want to use three separate tests instead of ANOVA?

Question 2:

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005).Based on pretreatment depression scores, patients were divided into four groups based on their level of depression.After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study. (data found in the pictures attached).

This is the summary table for the ANOVA test: (table also found in the pictures attached)

From this table, you obtain the necessary statistics for the ANOVA:

F-ratio:4.7469239542858

p-value:0.00291

?2=0.036492270643269

a) What is your final conclusion?Use a significance level of?=0.01.

• These data do not provide evidence of a difference between the treatments.
• There is a significant difference between treatments.

b) Explain what this tells us about the equality of means.

c) Let's look at the boxplot for each treatment: (box plot in the pictures attached)

How could boxplots refine our conclusion in an ANOVA test? Answer should address this specific problem.

. Question 1 5 pts ) 1 Suppose we want to test whether or not three population means are equal. We can assume the population variances are equal and there is only one factor of difference. We want to perform this test with a 1% significance level. If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type | error )? Suppose we, instead, run three separate hypothesis tests (t-tests), each with 1% significance level. o Mean 1 = Mean 2 o Mean 1 = Mean 3 o Mean 2 = Mean 3 What is the probability that all three tests would be accurate? Hint: use principles of probability to help your calculations: P(accurate AND accurate AND accurate) (Write your answer accurate without rounding.) Why would we use ANOVA instead of three separate tests? Edit * Insert Formats B / U x x A - Why would we want to use three separate tests instead of ANOVA? Edit * Insert * Formats . B / U x x|A -0 Question 2 an; ~01 Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study. Low High Moderately Moderate Hederete Severe 1.3 1.1 2.8 3.3 3.8 1 .7 1.3 2.8 0.7 2.6 2.9 3.2 1.4 2 0.7 1 1.6 3.8 1 . 2 0.7 0.3 0.4 1.1 3.1 1.2 3 0.9 3.1 2.5 2.6 3.8 1.8 1.6 3.3 3 2.7 0.3 1.4 1.3 2.8 1.9 2.8 3.2 3.9 3.4 2.8 1.2 4.1 0.7 1.1 3.4 2.3 1.6 0.2 2.4 3.1 2.7 2 2.6 1.1 3.1 2.7 3.9 0.5 0.1 2.1 2.8 2.5 2 2.7 2.2 0.7 1 2.3 1 3.3 3 3 0.5 2.3 1.1 1.5 1.5 1.2 0.4 2.2 1.4 2.2 1.8 1.2 1.2 1.4 1.1 1.7 0.9 2.9 1.5 3.4 1.1 2.3 2.6 1.4 0.2 2.8 3.1 3.8 0.8 1.7 4.7 0.9 3.8 1.9 2.2 1.1 1.2 2.8 2.8 2.5 2.7 2.9 3.8 1 .6 1.8 3.5 2.4 3.5 1 2.5 3 3.1 1.2 3.4 0.7 2.2 0.6 3.5 0.7 0.8 3.1 0.3 2.7 3.1 3.2 2.6 2.8 3.1 2.3 3.1 0.8 2.3 2.6 1 0.9 1.2 2.8 1.7 2.8 1.7 1.4 2 3.8 2.1 2.1 2.3 0 0 2.2 3.3 2.9 0.2 4.4 1.2 2.1 2 1 0.8 1.8 3.2 0.7 2 1.4 3.6 2.1 1.7 1.5 2.7 3.1 2.5 3 2.2 3.6 0.9 1.6 1.3 4 1.4 4.1 2.1 2.8 1.3 1.3 1.4 3.2 0.4 0.2 1.8 3.6 1 .7 1.6 0.4This is the summary table for the ANOVA test: S. S. d.f. M.S Between 14.095868421052 3 4.6986228070175 Within 372. 17410526316 376 0.98982474804031 TOTAL 386.26997368421 379 From this table, you obtain the necessary statistics for the ANOVA: F-ratio: 4.7469239542858 p-value: 0.00291 72 = 0.036492270643269 What is your final conclusion? Use a significance level of a = 0.01. These data do not provide evidence of a difference between the treatments OThere is a significant difference between treatments Explain what this tells us about the equality of means. Edit " Insert Formats * B / U X, x A Let's look at the boxplot for each treatment: Severe Moderately Severe High Moderate Low Moderate Depression Scores How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific