Question

You must attempt all questions.

You must use Minitab and/or Excel to solve all questions.

Show all of your works.

State your hypothesis if required,

Do NOT give the numerical final answer only, you MUST comment on all of your final finding.

If required, use ?=0.05 for all the tests.

Q1) 10 points

A study of speeding violations and drivers who use cell phones produced the following fictional data:

	Speeding ticket	No speeding ticket
Uses cell phone while driving	40	280
Does not use cell phone while driving	45	205

Does getting a speed ticket or not depend on whether the drive uses his cell phone while driving or not?

Q2) 10 points

When deciding whether to admit a high school graduate student into university, colleges take lots of factors, such as High school grade point average, and Qiyas scores, into consideration. Using Qiyas scores as a basis of whether to admit a student or not has created some controversy. Among other things, people question whether the Qiyass are fair and whether they predict college performance.

To evaluate this controversy, a study examines the High school grade point average (high_GPA) and University GPA (univ_GPA) information of 50 students who graduated from a university with a B.S. in computer science. Using the high_GPA from high school, can you predict a univ_GPA?

Find the regression line for predicting the university GPA from the high school GPA.

What is the slope?

What is the y-intercept?

If someone had a 4.0 GPA in high school, what is the best estimate of his or her college GPA?

What is the coefficient of correlation between the students' university GPAs and their computer science GPAs?

What is the Coefficient of Determination of the model?

Assessing Model Utility by Making Inferences about b₁

Assessing Model Utility by Testing the population correlation coefficient

#	high_GPA	univ_GPA	#	high_GPA	univ_GPA	#	high_GPA	univ_GPA
1	3.34	3.42	19	2.24	2.34	37	3.28	3.48
2	3.68	3.6	20	3.29	3.29	38	3.42	3.44
3	2.84	2.4	21	3.41	3.4	39	3.9	3.59
4	2.74	2.83	22	3.56	3.38	40	3.12	3.28
5	2.71	2.38	23	3.61	3.28	41	2.83	3
6	2.24	3.21	24	3.28	3.31	42	2.09	3.42
7	2.48	2.24	25	3.21	3.42	43	3.17	3.41
8	3.14	3.4	26	3.48	3.39	44	3.28	3.49
9	2.83	3.07	27	3.62	3.51	45	3.02	3.28
10	3.44	3.52	28	2.92	3.17	46	3.42	3.17
11	2.89	3.47	29	2.81	3.2	47	3.06	3.24
12	2.67	3.08	30	3.11	3.41	48	2.76	2.34
13	3.24	3.38	31	3.28	3.29	49	3.19	3.28
14	3.29	3.41	32	2.7	3.17	50	3.11	3.41
15	3.87	3.64	33	2.62	3.12
16	3.94	3.71	34	3.72	3.71
17	3.42	3.01	35	3.42	3.5
18	3.52	3.37	36	3.51	3.34

Q3) 10 points

Calcium is an essential mineral that regulates the heart, is important for blood clotting and for building healthy bones. The National Osteoporosis Foundation recommends a daily calcium intake of 1000-1200 mg/day for adult men and women. While calcium is contained in some foods, most adults do not get enough calcium in their diets and take supplements. Unfortunately some of the supplements have side effects such as gastric distress, making them difficult for some patients to take on a regular basis.

A study is designed to test whether there is a difference in mean daily calcium intake in adults with normal bone density, adults with osteopenia (a low bone density which may lead to osteoporosis) and adults with osteoporosis. Adults 60 years of age with normal bone density, osteopenia and osteoporosis (6 for each group) are selected at random from hospital records and invited to participate in the study. Each participant's daily calcium intake is measured based on reported food intake and supplements. The data are shown below.   

Is there a statistically significant difference in mean calcium intake in patients with normal bone density osteopenia and osteoporosis?

Runs    Treatments	Calcium Intake
	1	2	3	4	5	6
Normal Bone Density	1000	1100	980	900	800	900
Osteopenia	900	1000	700	950	500	850
Osteoporosis	890	650	1100	550	400	350

Q4) 10 points

The following experiment is interested in comparing the effect four different chemicals (A, B, C and D) in producing water resistance (y) in textiles. A strip of material, randomly selected from each bolt, is cut into four pieces (samples) the pieces are randomly assigned to receive one of the four chemical treatments. This process is replicated three times producing a Randomized Block (RB) design. Moisture resistance (y) were measured for each of the samples. (Low readings indicate low moisture penetration). The data is given in the following table:

	Blocks (Bolt Samples)
Chemical	1	2	3
A	10.1	11	10.9
B	12	12.8	11.5
C	11	12.3	11.4
D	12.1	11.8	12.9

Is there any affect for the chemicals types?

Is there any affect for the bolts?

Answer 1

Q1)

we use chi-square test of independence

Ho: both variables are independent

Ha: both are not independent

		c1	c2	total
	r1	40	280	320
	r2	45	205	250
	total	85	485	570
	Oi	40	280	45	205
	Ei	47.7193	272.2807	37.2807	212.7193
						TS
	(O--Ei)^2/Ei	1.24871	0.218846	1.598349	0.280123	3.346028
	critical value	3.84
p-value	0.067367391

TS = 3.34602

critical value = 3.84

since TS < critical value

we fail to reject the null hypothesis

there is not sufficient evidence that speed ticket depend on whether the drive uses his cell phone while driving or not.

Excel formulation

		c1	c2	total
	r1	40	280	=D4+E4
	r2	45	205	=D5+E5
	total	=D4+D5	=E4+E5	=F4+F5
	Oi	=D4	=E4	=D5	=E5
	Ei	=D7*F4/F7	=E7*F4/F7	=D7*F5/F7	=E7*F5/F7
						TS
	(O--Ei)^2/Ei	=(D9-D10)^2/D10	=(E9-E10)^2/E10	=(F9-F10)^2/F10	=(G9-G10)^2/G10	=SUM(D12:G12)
	critical value	3.84
p-value	=1 - CHISQ.DIST(H12,1,1)