Please I need only right answers.. Please help me solve these problems.. Thank y
ID: 3367560 • Letter: P
Question
Please I need only right answers.. Please help me solve these problems.. 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#1(25 marks)
Sample_BMI
34.74 16.79 25.29 30.98 29.73 20.78 26.15 28.49 28.58
31.95 38.57 26.70 22.12 33.18 24.14 23.56 22.35 22.11
30.34 33.55 26.49 22.28 25.63 29.35 30.45
a. A sample of size 25 has already been drawn and given above. This column is named 'Sample_BMI'. Calculate manually and find a 95% confidence interval for this population BMI. Explain what it means?
b. Based on the data in 'Sample_BMI', test the hypothesis that the population mean is less than 29.50. Use a level of significance of 5%.
c. Calculate the appropriate asymmetrical confidence interval or bound for the the test you performed in part 'b'. Explain if this calculated bound is consistent with the conclusion you reached in your test.
d. You want to estimate the average BMI of the population. If you want to calculate a 98% confidence interval with a margin of error of ± 0.75 units of BMI, what sample size would you recommend? Assume for this subquestion in part 'd', that the population standard deviation of BMI is 6.0 units.
e. 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?
Explanation / Answer
Using MiniTab
a. A sample of size 25 has already been drawn and given above. This column is named 'Sample_BMI'. Calculate manually and find a 95% confidence interval for this population BMI. Explain what it means?
----> Stat---> Basic Statistics ----> 1-Sample t
One-Sample T: Sample_BMI
Variable N Mean StDev SE Mean 95% CI
Sample_BMI 25 27.37 5.05 1.01 (25.29, 29.46)
That means we have 95% confidence that population_BMI mean belong to 25.29 to 29.46
b. Based on the data in 'Sample_BMI', test the hypothesis that the population mean is less than 29.50. Use a level of significance of 5%.
---->
One-Sample T: Sample_BMI
Test of ? = 29.5 vs < 29.5
Variable N Mean StDev SE Mean 95% Upper Bound T P
Sample_BMI 25 27.37 5.05 1.01 29.10 -2.11 0.023
Conclusion : P-value is less than 0.05 so we reject Ho
c. Calculate the appropriate asymmetrical confidence interval or bound for the test you performed in part 'b'. Explain if this calculated bound is consistent with the conclusion you reached in your test.
-----> bound for the test is 29.10
d. You want to estimate the average BMI of the population. If you want to calculate a 98% confidence interval with a margin of error of ± 0.75 units of BMI, what sample size would you recommend? Assume for this subquestion in part 'd', that the population standard deviation of BMI is 6.0 units.
----->
Here we want to find out sample size(n)
Given : s=6 , E=0.75 ,Z=1.28
n=((Z *s)/E)^2
=((1.28*6)/0.75)^2
=104.8576
=105
105 the sample size required for the 98% confident interval
Best of luck :)
We will give you only 4 bit solution because of chegg rule