Complete the classical six-step hypothesis testing method. using the lab demo as
ID: 3216849 • Letter: C
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