Quantitative Data Analysis Exercise

1) For the following data ranging from 0-20, construct a histogram:

1 2 2 2 3 3 4 5 5 5 6

6 6 6 6 7 7 7 8 8 8 8 9 9

9 9 9 9 9 10 10 10 10 10 10 11 11

11 11 11 11 11 12 12 12 12 12 13 13 13

14 14 14 15 15 16 16 16 17 17 17 18 18

19 20

2) For the data set in Question 1, calculate the mean, median, mode, variance, and standard deviation. Consider the data set as a population when calculating variance and standard deviation.

3) For the following sample data set, calculate the mean, variance, and standard deviation:

158

191

132

184

166

142

185

196

174

188

185

174

163

152

141

4) For the following sample data set, calculate the mean, variance, and standard deviation:

181

186

178

172

188

165

146

186

174

190

144

183

173

169

170

5) If the stated research (alternate) hypothesis is that there is a difference between the data sets from Question 3 and Question 4, the corresponding null hypothesis is that there is no difference between the data sets from Question 3 and Question 4. Compare the data sets from questions 3 and 4 using a non-directional (two-tailed) t test for independent means. From your calculations what are the degrees of freedom, t-statistic, and corresponding p-value? Provide a p-value plot (from StatCrunch options), as well as Summary Statistics (n, mean, standard deviation).

6. Using the data from questions 3 and 4 (displayed below), consider the following problem set-up. A physiologist wants to evaluate whether or not a treatment causes an observed measurement to significantly increase. Using a paired t test, the physiologist observes a measurement from 15 participants, administers a treatment, and then takes another measurement to see the impact of the treatment. The research hypothesis is that participants who receive the treatment have an increase in the second observation. The null hypothesis is that there is no difference between the first and second observation.

Observation 1 (pre-treatment)	Observation 2 (post-treatment)
158 191 132 184 166 142 185 196 174 188 185 174 163 152 141	181 186 178 172 188 165 146 186 174 190 144 183 173 169 170

Using the five-step problem solving process and statistical software, conduct a one-tail t test for dependent means (sometimes called repeated measures or paired), to provide the following information.

a. What is the hypothesis? What is the null?

b. What are the mean and standard deviation for each set of measurements (observation 1 and observation 2)?

c. What are the degrees of freedom, and the t-critical cutoff score at the .05 level?

d. What is the observed t-statistic? What is the corresponding p-value?

e. Based on the p-value, what is your conclusion on the null hypothesis (reject or fail to reject)?

f. What is your recommendation about the effectiveness of the treatment?

7. The following two groups are being compared to see if there is a difference in their test scores. Group 1 completed a training program and their final performance scores were recorded. Group 2 completed our new training program and their final performance scores were recorded. Did the new training program result in statistically improved scores? Draft a hypothesis and corresponding null hypothesis. Conduct a t test for independent means, present the mean and standard deviation for each group, and the t-statistic and p-value. State your conclusion.

Group 1	Group 2
76	97
88	91
91	93
79	92
69	83
79	86
88	88
85	89
84	92
82	79
91	93
86	85
76	86
96	89
78	77
71	79
59	61
86	64
82	88
83	89
79	92
76	95
91	88
93	79
67	76
69	88
86	91
81	96
82	93
92	92

8. In an attempt to identify which of three methods produces the best results for converting sunlight into electricity for a new satellite solar panel design, the following conversion efficiency scores (higher is better) are reported for the three designs. Using an Analysis of Variance Test, determine if there is a statistically significant difference among any of the designs. State the hypothesis, null hypothesis, and present the summary descriptive statistics, as well as the F-statistic and p-value. State your conclusions.

Design 1	Design 2	Design 3
17	19	17
19	26	21
14	25	20
19	25	21
18	28	20
16	27	19
15	24	20

9. To evaluate the effects of a new policy, complete a regression analysis to determine if there is a statistically significant correlation between the number of STEM classes required in an undergraduate degree program and the percentage of those students entering STEM jobs immediately after graduation.

Degree Program	STEM Courses Required (x)	% Entering STEM Jobs (y)
A	15	69
B	11	57
C	9	50
D	6	28
E	10	48
F	4	12
G	8	52
H	3	7
I	9	40
J	7	42

10. Our marketing department is trying to better understand the preferences of customers to inform the redesign of the coach seating on our aircraft. 150 participants looked at mock-ups of the redesign, and were asked their preference of fabric color. Evaluate the data below using a chi-square goodness of fit test, and determine if any of the colors were clearly preferred by the participants. Keep in mind, the hypothesis would be that one of the colors is preferred, while the null hypothesis would be that there is no preference (all counts are the same). What are your conclusions?

Color	Count Indicated as Preferred by Participant
Light Blue	23
Dark Blue	37
Gray	58
Platinum	20
Pearl	12