Question

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.

Sample_BMI

34.74
31.95
30.34
16.79
38.57
33.55
25.29
26.70
26.49
30.98
22.12
22.28
29.73
33.18
25.63
20.78
24.14
29.35
26.15
23.56
30.45
28.49
22.35
28.58
22.11

Test the hypothesis that the population median of the BMI is other than 29.50. Also, find the 95% Confidence Interval for this population median. Is it consistent?

Please use Minitab to show your work and tell me the steps in Minitab

Answer 1

Null hypothesis : H_o : population median of the BMI is 29.50

Alternate hypothesis : H_a : population median of the BMI is other than 29.50 ; median of the BMI 29.50

Sign Test for Median: Sample-bmi

Sign test of median = 29.50 versus ≠ 29.50

Step1 : Enter the Data into one of the columns of work sheet in Minitab

Step 2 : Select Stat-> Nonparametrics->1-Sample sign

Step 3 : Select "Sample-BMI" Under variables and for hypothesis testing; select radio button Test Median and enter 29.5 in the cell ; And select Alternatve as "not equal" and press "ok"

Step4: The results are displayed in sessions window.

The p-value from the sessions window : 0.2295;

As p-value is :0.225 >

Fail to reject null hypthesis.

Not enough evidence to conclude that median is not 29.50.

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Confidence interval;

Follow step1 and step 2 as above;

Step3 : Step 3 : Select "Sample-BMI" Under variables and for Confidence interval ; select radio button Confidence interval and enter 95.0 in the cell Confidence inteval cell and press "ok"

Step4: The results are displayed in sessions window.

From the session window you can observe that the 95% confidence interval for median :

(24.37, 30.22);

As Hypothesied median : 29.50 is withtin in the 95% confidence interval (24.37, 30.22);

It is consistent with the hypothesis testing result.