Question

Student	What is your height in inches?	What is your weight in pounds?	What is your cumulative Grade Point Average (GPA) at FTCC or your primary college?	How many hours do you sleep each night?
1	67	100	4	7
2	62	105	4	5
3	72	120	4	8
4	61	125	4	7
5	56	105	3.7	6
6	61	120	4	7
7	65	172	3.8	7
8	72	235	3.22	5
9	63	135	4	6
10	71	182	3.62	6
11	70	172	4	6
12	72	160	2.3	8
13	67	135	4	8
14	64	128		7
15	72	180	2.5	8
16	70	170	4	6
17	63	210	3.75	4
18	68	180	2.2	7
19	72	250	3.69	6
20	76	210	1.98	6
21	63	144		6
22	68	165	2.5	6
23	64	140	3.7	9
24	69	145	3	5
25	72	270	2.5	7
26	63	132	4	7
27	63	148	3.231	5
28	72	185	3.5	6
29	69	175	4	6
30	59	155	3.6	7
31	69	179	4	8
32	62	205	3.5	6
33	63.5	180	3.7	5
34	68	240	4	5
35	62	168	3.3	7
36	67	137	3.2	8
37	70	200	4	6
38	69	186	4	5
39	60	140	4	5
40	70	199	3.8	5
41	65	205	2.5	10
42	65	145	3.2	8
43	72	180	2.1	6
44	74	175	3.5	7
45	67	140	3.7	6
46	70	215	3	8
47	67	205	2.8	6
48	68	191	3.51	8
49	71	213	1.4	4
50	71	225	2.7	6
51	70	217	3.8	6
52	67.2	150	4	6
53	71	190	1.7	8
54	76	220	3.7	7
55	68	189	3.5	8

Part 3:

In Module 3, we looked at the hours of sleep that FTCC students get each night. I found online that the average hours of sleep that an adult gets is 6.8 hours. Does this seem likely based on our sample of students? You should show all work supporting this claim and write a paragraph explaining your decision.

You can use Intervals or Hypothesis testing to prove or disprove this claim. You will choose the confidence level or significance level.

Show all steps in the chosen process.

If you do a hypothesis test, include the claim, hypothesis, significance level, so on…

If you do an interval, give confidence level, margin of error, so on…

Explain your reasoning in detail. Why do you think that the average is 6.8 hours or not 6.8 hours? Back up your opinion using the statistical information.

You should write one paragraph explaining the results of your statistical process.

Answer 1

Let be the true average hours of sleep that FTCC students get each night. We want to test the claim that the true average hours of sleep of FTCC students is different from 6.8 hours. In other words we want to test the claim that

The following are the hypotheses that we want to test

We have the following sample information about FTCC students

n=55 - sample size

hours is the sample mean hours of sleep

The spreadsheet to calcultae the above are

We do not know the standard deviation of the population hours of sleep of FTCC students. We estimate if using the sample standard deviation. The population standard deviation is

Next we calculate the standard error of mean as

The hypothesized value of mean hours of sleep is

The sample size is greater tnan 30. Hence this is a large sample analysis. We will use z-scores as sample statistics.

The test statistics is

This is a 2 tail test. The critical value of region is  for left tail is and for the right tail it is . That is we reject the null hypothesis if the test statistics of -1.73 is outside the interval  

The level of significance . The critical value is

This is same as

. Using standard normal tables we get

We will rejetc the null hypothesis if the test statistics is not in the interval [-1.96,1.96]

Since the test statistics -1.73 lies within the interval, we accept the null hypothesis.

We conclude at 95% confidence level that there is no sufficient evidence to support the claim that the average hours of sleep that FTCC students get each night is not equal to 6.8 hours.