Testing a Hypothesis about a Population Mean

Purpose:  Show ability to explain and carry out a hypothesis test to check a claim about a population mean.  

Background and Data: 

A lot has been written about students not getting enough sleep.  The National Sleep Foundation suggests that 7-9 hours of sleep per night is ideal for adult good health (http://www.sleepfoundation.org/article/how-sleep-works/how-much-sleep-do-we-really-need).

In the spring semester, data was collected to check sleep habits of day students on the Bedford campus at Middlesex Community College. 

Question:  “On average, about how many hours do you sleep per night?”

Claim:  Daytime students on the Bedford campus of Middlesex Community College sleep fewer than 7 hours per night. 

Data:  50 randomly selected Middlesex daytime students answered:

1	Mike	7.5		26	Jill	6
2	Jake	6		27	Reggie	8
3	Ray	7		28	Victor	6
4	Tom	6.5		29	George S.	7
5	Emma	4.5		30	Mike M.	6.5
6	Shauna	5		31	Milly	6
7	Britney	8.5		32	Aaron	5
8	Timothy	6		33	Tim	6
9	Matt	8		34	Marina	9
10	Heather	7.5		35	Shirley	6.5
11	Jaime	8		36	Mitchell	8
12	Veronica	7		37	Carol	7
13	Greg	6		38	Paul	8
14	Michael	6.5		39	Veronica W.	7
15	Will	7.5		40	Edmond	5
16	Zoe	8.5		41	Leslie	8
17	Jess	8		42	Steve	7.5
18	Lara	6.5		43	Mitchell	6
19	Henry	8		44	Kirstin	6
20	George	7		45	Stephen	4
21	Edwin	5		46	Rebecca	9
22	Jessica	6		47	Stephen	7.5
23	Michele	4.5		48	Anne	5
24	Andy	6		49	Tara	4.5
25	Mike T.	5.5		50	Mike P.	7

Tasks: 

·         Enter the given data in a calculator list.  Be careful and accurate.

·         Formulate the two hypotheses to test the given claim (see claim above)

·         Choose the appropriate test and carry it out  

·         Fill out the attached summary form and include the three required calculator screens as illustrated on the form.  TI-Connect is needed.

·         The Math centers in Bedford and Lowell are open Monday through Thursday 10AM-6PM.

·         Write a one to two-page analysis explaining the concepts of hypothesis testing to a reader who is not familiar with Statistics.  Use these concepts (not your personal opinion) to justify your conclusion.  I attached a list of questions to guide your analysis.  

·         The final document consists of the summary page, followed by the analysis or answers to the given questions.  The project could be 2 to 3 pages long.  I am looking for completeness and clarity rather than quantity.  So, writing 4 pages is not necessarily better than 2 or 3.  

In your analysis, please address in your own words (do not copy definitions) the following questions. 

1.    What is a null hypothesis?  What is an alternative hypothesis?  How does one recognize whether a hypothesis is a null hypothesis or an alternative one?  What role does each of them play? 

2.    Explain the meaning of significance level.

3.    What is the rejection region? How is it related to the significance level? 

4.    What is the meaning of P-value?  What is the advantage of using the P-value method?

5.    List the statistical requirements needed for your test (see requirements on p. 433 of the text) and explain which of them are or are not satisfied in this project.

6.    Explain your conclusion about rejecting or not rejecting H_o so a non statistician would understand.  When is it correct to say that the test is significant? 

7.    Do Middlesex daytime students sleep on average fewer than 7 hours per night?

8.    What is type I error in this context?