Testing for differences in student height

Question

Complete the following:

1. Describing the Data

a) Identify each of the variables in the dataset and describe what type of variable they are (i.e. categorical, discrete numerical, ordinal, etc.). The easiest way to do this is make a list, top to bottom, of variables, their type, and your justification for calling them this type. DON'T FORGET TO justify your answers (i.e. why is this a "categorical" variable?).

b) For the numerical data, create a table of summary statistics. Include columns for AT LEAST the mean, standard deviation, median, minimum, and maximum. Define each of these terms (e.g. in statistics, what is a "mean?").

2. Sixth grade students are randomly put into classrooms every year. Three students, Michael Miller, Jose Rodriguez, and Scott Perez are best friends and want to be in the same class.

a) What is the probability that they are all in the same class?

b) What is the probability that they are all in Mr. Collins' class?

c) What is the probability that they are all in different classes?

3. There are 100 students overall, and they are distributed into 4 classrooms of equal size. There are 54 girls and 46 boys in sixth grade at Oceanview. Calculate the probability that:

a) A class will have 15 girls

b) A class will have 15 boys

c) A class will have more than 20 girls

4. Student Height and the Normal Distribution.

a) Construct a histogram of the students' height in centimeters.

b) Use the histogram and any other statistical tools that might be useful to determine if the distribution is normal. IMPORTANT! YOU MUST USE AT LEAST THREE PIECES OF EVIDENCE (any of the 6 we learned in class) TO DETERMINE WHETHER THE DISTRIBUTION IS NORMAL.

c) Construct a histogram of the students' height in inches.

d) Use the histogram and any other statistical tools that might be useful to determine if the distribution is normal. IMPORTANT! YOU MUST USE AT LEAST THREE PIECES OF EVIDENCE (any of the 6 we learned in class) TO DETERMINE WHETHER THE DISTRIBUTION IS NORMAL.

e) The data series are obviously related…the students' heights were measured in centimeters and that was converted to inches. What gives rise to any discrepancies you see, particularly in the shape of the histogram?

5. Testing for differences in student height.

a) The average height of 6th grade girls in the state of Kansas is 61.8 inches, and the average height of 6th grade boys in the state of Kansas is 59.4 inches. Are the heights of the boys and girls at Oceanview statistically different from the statewide averages? On what objective, statistical evidence do you base your answer here? IMPORTANT! PROVIDE THE EVIDENCE AND INTERPRET IT IN NARRATIVE.

b) Is there a statistically significant difference between male and female height among sixth graders at this school? On what objective, statistical evidence do you base your answer here? IMPORTANT! PROVIDE THE EVIDENCE AND INTERPRET IT IN NARRATIVE.

6. Teacher Quality

a) Calculate and compare the means of student test scores by class.

b) Test to see if the differences in test scores are statistically significant (remember to provide the evidence and INTERPRET the evidence, in narrative form. Then, if applicable, determine: Which teachers have better performing students than others? Which have worse performing students?

c) Can your evidence be used as conclusive evidence that some of the teachers are better/worse at teaching than others? Why or why not?

d) Repeat steps a and b using IQ scores instead of test scores. Does this change your response to part c? If so, how so? If not, why not?

e) The statewide average on the standardized test is 75. First, assume that you do not know the standard deviation for the population.

How well does the school perform relative to the state average? How well does each teacher perform relative to the state average? Remember to provide objective, statistical evidence to back your claim, and INTERPRET the evidence, in narrative.

f) Repeat step e, this time using the fact that the statewide standard deviation of test scores is 8.

g) In parts e and f, correctly name the null and alternate hypotheses. Given those hypotheses, what would constitute a type I or a type II error? Did discovering the true population standard deviation in part f reveal any type I or type II errors in part e?

7. Intelligence and Test scores

a) Construct a scatter plot of IQ scores and test scores (use IQ as your independent variable and test score as your dependent variable).

b) Estimate the relationship between IQ and test scores using regression analysis

c) Interpret the meaning, both in the abstract and specifically related to this problem, of the Y intercept and beta coefficient. Are the results statistically significant? How do you know? On what evidence do you base your conclusion?

d) IQ is surely not the only determinant of student test scores. Estimate the relationship between class attendance, measured as days missing from class, and test scores.

e) Interpret the Y intercept and beta coefficient. Are the results statistically significant? How do you know? On what evidence do you base your conclusion?

f) Estimate test scores using BOTH IQ and attendance as independent variables. How do these relate to your answers to b-e?

g) Speculate: Are there other variables (i.e. ones not in the dataset) you think might be correlated with test scores? Why or why not? On what evidence do you base your claim here?

id	Last	First	Height (cm)	Height (inches)	Gender	Teacher	Test Score	IQ	Days Missed
1	Smith	Linda	157	62	Female	Marshall	78	92	1
2	Johnson	Bonnie	158	62	Female	Lopez	78	71	7
3	Williams	Erika	151	59	Female	Marshall	77	113	5
4	Jones	Melissa	150	59	Female	Collins	76	119	6
5	Brown	Jennifer	156	61	Female	Marshall	82	101	6
6	Davis	Steven	155	61	Male	Weinberg	80	92	4
7	Miller	Michael	156	61	Male	Collins	70	88	1
8	Wilson	Elizabeth	147	58	Female	Weinberg	70	146	5
9	Moore	Lisa	156	61	Female	Collins	60	88	8
10	Taylor	Nancy	158	62	Female	Collins	92	111	1
11	Anderson	Karen	146	57	Female	Weinberg	77	125	3
12	Thomas	James	149	59	Male	Marshall	75	95	6
13	Jackson	Sandra	167	66	Female	Lopez	84	115	6
14	White	John	153	60	Male	Lopez	71	96	11
15	Harris	Sarah	161	63	Female	Lopez	80	104	8
16	Martin	Jessica	166	65	Female	Lopez	90	92	2
17	Thompson	Amy	156	61	Female	Lopez	78	85	8
18	Garcia	Anna	160	63	Female	Marshall	82	117	3
19	Martinez	Janet	160	63	Female	Marshall	96	95	1
20	Robinson	Robert	160	63	Male	Weinberg	82	109	10
21	Clark	Julie	151	59	Female	Weinberg	78	103	7
22	Rodriguez	Jose	159	63	Male	Weinberg	70	114	8
23	Lewis	Joseph	151	59	Male	Lopez	95	124	3
24	Lee	Chris	150	59	Male	Collins	53	92	6
25	Walker	Stephanie	164	65	Female	Lopez	74	135	9
26	Hall	Nicole	149	59	Female	Weinberg	69	68	7
27	Allen	Daniel	154	61	Male	Weinberg	62	81	5
28	Young	Theresa	151	59	Female	Marshall	69	102	3
29	Hernandez	Anthony	153	60	Male	Weinberg	83	112	0
30	King	Lori	163	64	Female	Marshall	87	78	3
31	Wright	Kevin	160	63	Male	Marshall	96	115	3
32	Lopez	Andrea	146	57	Female	Lopez	65	98	6
33	Hill	Matthew	143	56	Male	Marshall	77	99	5
34	Scott	Timothy	150	59	Male	Weinberg	78	84	10
35	Green	Crystal	162	64	Female	Weinberg	86	78	3
36	Adams	Ruby	159	63	Female	Weinberg	71	99	12
37	Baker	Eric	152	60	Male	Collins	82	72	3
38	Gonzalez	Miguel	149	59	Male	Weinberg	73	112	4
39	Nelson	Tracy	159	63	Female	Weinberg	71	67	8
40	Carter	Edna	163	64	Female	Lopez	75	94	6
41	Mitchell	Sylvia	157	62	Female	Collins	71	84	2
42	Perez	Scott	161	63	Male	Collins	43	84	12
43	Roberts	Peter	151	59	Male	Weinberg	69	132	2
44	Turner	Wendy	159	63	Female	Collins	68	76	10
45	Phillips	Henry	153	60	Male	Collins	59	86	4
46	Campbell	Cindy	151	59	Female	Collins	74	93	11
47	Parker	Shannon	164	65	Female	Marshall	65	112	6
48	Evans	Anita	155	61	Female	Lopez	71	110	0
49	Edwards	Ryan	160	63	Male	Marshall	82	92	5
50	Song	Eva	160	63	Female	Marshall	71	105	7
51	Stewart	Jamie	154	61	Female	Lopez	71	69	12
52	Sanchez	Albert	155	61	Male	Weinberg	78	76	6
53	Morris	Justin	162	64	Male	Lopez	80	102	10
54	Rogers	Megan	155	61	Female	Collins	51	79	13
55	Reed	Keith	157	62	Male	Weinberg	69	128	2
56	Cook	Carlos	161	63	Male	Lopez	73	129	5
57	Morgan	Russell	150	59	Male	Collins	69	101	3
58	Bell	Adam	158	62	Male	Weinberg	90	117	2
59	Murphy	Billy	157	62	Male	Lopez	74	98	4
60	Bailey	Alicia	156	61	Female	Collins	64	102	5
61	Rivera	Randy	155	61	Male	Lopez	87	103	8
62	Cooper	Emma	157	62	Female	Marshall	76	86	8
63	Richardson	Victor	156	61	Male	Collins	69	101	3
64	Cox	Melanie	154	61	Female	Marshall	81	99	11
65	Howard	Brittany	144	57	Female	Marshall	72	74	10
66	Ward	Shawn	153	60	Male	Weinberg	52	76	8
67	Torres	Dale	162	64	Male	Lopez	86	111	4
68	Peterson	Beth	158	62	Female	Collins	62	94	9
69	Gray	Alan	152	60	Male	Marshall	68	107	6
70	Ramirez	Danny	164	65	Male	Lopez	80	81	8
71	James	Sue	149	59	Female	Lopez	84	124	1
72	Watson	Bryan	147	58	Male	Weinberg	68	81	6
73	Brooks	Juanita	155	61	Female	Marshall	99	87	7
74	Kelly	Philip	148	58	Male	Marshall	95	133	5
75	Sanders	Eileen	155	61	Female	Collins	70	109	7
76	Price	Glenn	144	57	Male	Marshall	61	90	2
77	Bennett	Antonio	149	59	Male	Collins	72	120	3
78	Wood	Tonya	154	61	Female	Lopez	83	107	2
79	Barnes	Travis	145	57	Male	Weinberg	67	89	9
80	Ross	Maureen	161	63	Female	Collins	50	109	9
81	Henderson	Colleen	155	61	Female	Weinberg	64	94	12
82	Coleman	Lydia	153	60	Female	Lopez	80	124	4
83	Jenkins	Heidi	158	62	Female	Weinberg	91	145	5
84	Perry	Jacob	152	60	Male	Lopez	91	106	6
85	Powell	Lee	165	65	Male	Weinberg	59	114	6
86	Long	Jackie	152	60	Female	Marshall	71	103	6
87	Patterson	Leah	147	58	Female	Collins	56	62	7
88	Hughes	Edwin	153	60	Male	Lopez	80	114	6
89	Flores	Miriam	154	61	Female	Collins	69	103	10
90	Washington	Troy	150	59	Male	Marshall	80	99	8
91	Butler	Mario	157	62	Male	Weinberg	77	100	8
92	Simmons	Felicia	161	63	Female	Lopez	72	81	9
93	Foster	Calvin	147	58	Male	Marshall	83	120	6
94	Gonzales	Violet	159	63	Female	Collins	76	111	1
95	Bryant	Kent	154	61	Male	Collins	80	86	6
96	Alexander	Lindsey	165	65	Female	Marshall	63	86	5
97	Russell	Rene	148	58	Male	Marshall	72	103	2
98	Griffin	Brooke	154	61	Female	Collins	65	98	4
99	Diaz	Esmerelda	156	61	Female	Collins	59	77	6
100	Hayes	Eddie	159	63	Male	Lopez	79	121	3