Please help me solve these problems.. answers must be correct.. Thank you.. Gene
ID: 3367561 • Letter: P
Question
Please help me solve these problems.. answers must be correct.. Thank you..
General Instructions:
When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and “Alternate” hypotheses, ii. S2: manually calculate value of the test statistic, iii. S3: specify the level of significance and the critical value of the statistic, iv. S5: use appropriate decision rule and then reach a conclusion about not rejecting or rejecting the null hypothesis. S5: If asked to calculate p–value,do so and relate the p-value to the level of significance in reaching your conclusion.
If you use MiniTab to perform the hypothesis test, you must paste the relevant output into your assignment. This output simply verifies and occasionally replaces the manual computation of the test statistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, to make your testing procedure standard and complete.
If Confidence Coefficient (CC) and Level of Significance (LS) are not specified, assume the default values of 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) and no more or no less, when calculations are done with a calculator.
Question#2 :
RE-Agenc1
RE-Agenc2
2652
2532
2820
2664
2592
2736
3024
2760
2904
2676
2736
2820
3168
3180
3024
2820
2772
2652
3180
2856
3150
2790
Two Real Estate Agencies, RE-Agenc1 and RE-Agenc2 evaluated properties chosen with two independent random samples of income properties. The evaluation data is given above and the values are in thousands of dollars. Assume unequal population variances when doing this question #1.
a. Test the hypothesis that there is no difference in the mean values of evaluations of the two real estate agencies. Use the 'Critical Value' approach.
b. Calculate the p-Value for this test. What conclusion would you draw?
c. Calculate the Confidence Interval for the difference in mean values of evaluation? Is it consistent with the conclusion reached in part ‘a’?
RE-Agenc1
RE-Agenc2
2652
2532
2820
2664
2592
2736
3024
2760
2904
2676
2736
2820
3168
3180
3024
2820
2772
2652
3180
2856
3150
2790
Explanation / Answer
a. Test the hypothesis that there is no difference in the mean values of evaluations of the two real estate agencies.
Here we have to test the hypothesis that,
H0 : mu1 = mu2 Vs H1 : mu1 not= mu2
where mu1 and mu2 are two population means of RE-agency1 RE-agency 2 respectively.
Assume alpha = level of significance = 0.05
This is the case of two sample t-test by assuming equal variance.
MINITAB step :
ENTER data into MINITAB sheet --> Stat --> Basic statistic --> 2-Sample t for the mean --> Each sample is in its own column --> Sample 1 : select Re-agency1 --> Sample 2 : select RE-agency 2 --> Options --> Confidence level : 95.0 --> Hypothesize difference : 0.0 --> Alternative hypothesis : not= --> Assume equal variances --> ok --> ok
Test statistic = 0.99
Critical value = 2.086 (by using statistical table)
b. Calculate the p-Value for this test. What conclusion would you draw?
P-value = 0.334
c. Calculate the Confidence Interval for the difference in mean values of evaluation? Is it consistent with the conclusion reached in part ‘a’?
95% confidence interval for difference in population mean is (-93.3, 261.7)
We can see that population mean = 0 is lies between confidence limit.
Accept H0 at 5% level of significance.
COnclusion : There is not sufficient evidence to say that there is no difference in the mean values of evaluations of the two real estate agencies.