# ANOVA Analysis and Five-Step Hypothesis Testing

Please see attached file for full problem description and table format. Please show all work.

1. Given the following data conduct a test of hypothesis to determine whether the block and the treatment means differ. Use the .05 significance level and:

a. State the null and alternate hypotheses for the treatments;

b. State the decision rule for the treatments;

c. State the null and alternate hypotheses for the blocks;

d. State the decision rule for the blocks;

e. Interpret the ANOVA table;

f. What is your decision regarding the two sets of hypotheses?

Treatment

Block 1 2 3

A 12 14 8

B 9 11 9

C 7 8 8

2. There are three hospitals in the Tulsa area. The following data show the number of outpatient surgeries at each hospital last week. At the .05 significance level , can we conclude that there is a difference in the mean number of surgeries performed among the three hospitals and in the mean number of surgeries by day of the week?

a. State the null and alternate hypotheses for the treatments;

b. State the decision rule for the treatments;

c. State the null and alternate hypotheses for the blocks;

d. State the decision rule for the blocks;

e. Interpret the ANOVA table;

f. What is your decision regarding the two sets of hypotheses?

Number of Surgeries Performed

Day St. Lukes St. Vincent Mercy

Monday 14 18 24

Tuesday 20 24 14

Wednesday 16 22 14

Thursday 18 20 22

Friday 20 28 24

3. An experiment is designed to study the effect of two factors on a stereo recording. The factors are the type of receiver (two brands) and the type of amplifier (four brands). For each combination of factor levels, three tests are performed in which decibel output is measured. A higher decibel output means a better result. The coded results are as follows:

Amplifiers

Receivers A B C D

R1 9 8 8 10

4 11 7 15

12 16 1 9

R2 7 5 0 6

1 9 1 7

4 6 7 5

a. At the .01 level of significance:

i. Is there an interaction between receivers and amplifiers?

ii. Is there and effect that is due to receivers?

iii. Is there an effect that is due to amplifiers?

b. Plot a graph of average decibel output for each receiver and each amplifier;

c. On the basis of a and b what conclusions can you reach concerning average decibel output?

https://brainmass.com/statistics/analysis-of-variance/anova-analysis-five-step-hypothesis-testing-155945

#### Solution Summary

This solution addresses the three scenarios and presents a null and alternative hypothesis. A test statistic is calculated and compared with the p-value to make a decision to either accept or reject the null hypothesis. All steps are shown.