Complete the classical six-step hypothesis testing method. using the lab demo as

Question

Complete the classical six-step hypothesis testing method. using the lab demo as an example, to determine if the group means are equal at the =0.05 significance level. (FYI: Location 1 = South Salt Lake; Location 2 = Salt Lake City; Location 3 = Murray; Location 4 = Park City). You can use r studio and show F statistics table and sommary

HomePrice

Location

174

1

150

1

140

1

155

1

182

1

151

1

148

1

145

1

130

2

186

2

167

2

156

2

172

2

190

2

168

2

165

2

132

3

145

3

139

3

135

3

124

3

152

3

179

3

147

3

175

4

201

4

191

4

194

4

210

4

200

4

220

4

199

4

HomePrice

Location

174

1

150

1

140

1

155

1

182

1

151

1

148

1

145

1

130

2

186

2

167

2

156

2

172

2

190

2

168

2

165

2

132

3

145

3

139

3

135

3

124

3

152

3

179

3

147

3

175

4

201

4

191

4

194

4

210

4

200

4

220

4

199

4

Explanation / Answer

Step 1. State the null and alternative hypotheses:

Null Hypothesis : H0 : 1 = 2 = 3 = 4

Alternative Hypothesis : Ha : The four given means are not equal .

Step 2. Choose the level of significance: alpha , the probability of making a Type I Error if H0 is true

alpha = 0.05

Step 3. Determine the critical values for the level of significance a ,

I am produce ANOVA table here for F - tests

Here critical values Fcritical = 2.9467

Step 4: Estimate.

F value for all 4 means = 17.46 and p - value = 1.37 X 10-6

Step 5. Compare the test statistic to the critical values.

Here we can say that F > Fcritical

Step 6. Write a conclusion.

For the given level of significance 0.05, we reject the null hypothesis . In our test ,w e take a sample size of 32 and proposed a null hypotheis that means for all given locations are same and we performed F - test on the sample and found that means are sihgnificantly different from each other.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Location 1 8 1245 155.625 214.5536 Location 2 8 1334 166.75 344.2143 Location 3 8 1153 144.125 278.4107 Location 4 8 1590 198.75 175.9286 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 13271.13 3 4423.708 17.46591 1.37E-06 2.946685 Within Groups 7091.75 28 253.2768 Total 20362.88 31

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