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 4:

In Module 3, we looked at the GPAs of FTCC students. I found online source that claims the average GPA of college students in the US is 3.11. 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 GPA is 3.11 or is not 3.11? Back up your opinion using the statistical information.

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

Answer 1

Here sample size is 55 ( >30), So we use z-test as follow.

Hypothesis

Null hypothesis :  

Alternative hypothesis :

test statistic:

here, s is a standered deviation, we calculated using formula

But in given data their are 2 missing value of observation 14 and 21. So first we fill these using regression method as

1) we compute regression equation excluding these 2 missing observation.

2) Use MS-Excel, Syntax as

Data Data Analysis Regression Inpute Y range ( GPA) Inpute X's Range Select output range ok

Result is as

From above result regression equation is as

Y(GAP) = 7.1098 - 0.0355*ht - 0.0047*wt - 0.079*sleep

Let, 2 missing observation values computed using above equation is as

missing value of 14^th obs. Y=7.1098-0.0355*64-0.0047*128-0.079*7 = 3.6832

missing value of 21^th obs. Y=7.1098-0.0355*63-0.0047*144-0.079*6 = 3.7225

Let, we enter these value in table. Then compute mean and s.d. using syntax

mean = AVERAGE(inpute range) AVERAGE(E2:E56) = 3.3965

Standered Deviation = STDEV.S(E2:E56) = 0.6857

Then test statistic is as

Table value of Z

These is a 2 tailed test, So we take for 5% l.o.s.

z_0.05/2 = z_0.025 = 1.96

The z?value that corresponds to –0.025 is –1.96, which is the lower critical z?value. The upper value corresponds to 1 – 0.025, or 0.975, which gives a z?value of 1.96. The null hypothesis of no difference will be rejected if the computed z statistic falls outside the range of –1.96 to 1.96.

But we see that, Calculated z value (3.0988) is lies outside range(-1.96 , 1.96). So we reject null hypothesis.

Conclusion:

Therefore population mean is not equal to 3.11. That is Claim goes to fail.

Confidence Interval For 5% l.o.s. :

=3.3965 +/- 0.1812

=(3.2153 , 3.577)