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Quantitative Data Analysis Exercise Name College of Aviation, Embry-Riddle Aeronautical University ASCI 693: Current Research Problems in Aviation/Aerospace Dr. Name Apr 16, 2023

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 Hint: Instructions for constructing a histogram in StatCrunch are in Quantitative Primer 1.

2) For the following two sample data sets, calculate the mean, variance, and standard deviation: SAMPLE 1 SAMPLE 2 158 181 191 186 132 178 184 172 166 188 142 165 185 146 196 186 174 174 188 190 185 144 174 183 163 173 152 169 141 170 Hint: Instructions for calculating mean, variance, and standard deviation in StatCrunch are in the Quantitative Video “StatCrunch: Getting Started”. Summary statistics: Column Mean Variance Std. dev. Sample 1168.73333406.9238120.172353 Sample 2173.66667192.5238113.875295 3) If the stated research (alternate) hypothesis is that there is a difference between the data sets from Sample 1 and Sample 2 in Question 2, the corresponding null hypothesis is that there is no difference between the data sets from Sample 1 and Sample 2 . Using StatCrunch: Compare the data sets from Sample 1 and Sample 2 using a non-directional (two-tailed) t test for independent means. Hint: Instructions for Hypothesis Testing Basics are in Quantitative Primer 4. Instructions for conducting a t test using StatCrunch can be found in Quantitative Primer 5 and the Quantitative Video “Conducting Hypothesis Testing for the Difference Between Two Means with Raw Data”. Two sample T hypothesis test: μ 1 : Mean of Sample 1 μ 2 : Mean of Sample 2

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μ 1 - μ 2 : Difference between two means H 0 : μ 1 - μ 2 = 0 H A : μ 1 - μ 2 ≠ 0 (with pooled variances) Hypothesis test results: DifferenceSample Diff. Std. Err. DF T-Stat P-value μ 1 - μ 2 -4.93333336.3216433 28-0.7803878 0.4417 From your calculations, what is your conclusion based on the p-value? Is there a statistically significant difference between the two samples? Based on the p-value of 0.4417, we cannot reject the null hypothesis at the standard significance level of 0.05. We do not have sufficient evidence to conclude that there is a statistically significant difference between the two samples. 4) 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 your conclusions. Hint: Instructions for conducting an ANOVA test using StatCrunch can be found in Quantitative Primer 6 and the Quantitative Video “One-Way ANOVA”. 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 H 0 : There is no significant difference among the mean conversion efficiency scores of the three solar panel designs. H A : At least one of the solar panel designs has a significantly different mean conversion efficiency score than the others. Analysis of Variance results: Data stored in separate columns.

Column statistics Column n Mean Std. Dev. Std. Error Design 1716.8571431.95180010.73771111 Design 2724.8571432.9113898 1.1004019 Design 3719.7142861.38013110.52164053 ANOVA table Source DF SS MS F-Stat P-value Columns 2230.09524115.0476224.322148<0.0001 Error 1885.1428574.7301587 Total 20 315.2381 Tukey HSD results (95% level) Design 1 subtracted from Difference Lower Upper P-value Design 2 8 5.033036110.966964<0.0001 Design 3 2.8571429-0.109821095.8241068 0.0602 Design 2 subtracted from Difference Lower Upper P-value Design 3-5.1428571-8.1098211-2.1758932 0.0009 Conclusion: The F-ratio for the ANOVA test is 24.32, indicating that there is strong evidence against the null hypothesis. Therefore, we can conclude that there is a significant difference among the mean conversion efficiency scores of the three solar panel designs. To determine which specific pairs of designs are significantly different, we can use Tukey's HSD test at the 95% level. According to the results of the Tukey HSD test, there is a significant difference between Design 1 and Design 2, and between Design 2 and Design 3. However, there is not enough evidence to reject the null hypothesis for the difference between Design 1 and Design 3. 5) 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?

Hint: Instructions for conducting a chi-square test using StatCrunch can be found in Quantitative Primer 7 and the Quantitative Video “Creating a Contingency Table from Summary Data”. Color Count Indicated as Preferred by Participant Light Blue 23 Dark Blue 37 Gray 58 Platinum 20 Pearl 12 Chi-Square goodness-of-fit results: Observed: Count Indicated as Preferred by Participant Expected: All cells in equal proportion N DFChi-SquareP-value 150 4 43.533333<0.0001 Observed Expected 23 30 37 30 58 30 20 30 12 30 With 4 degrees of freedom, the critical chi-square value at a significance level of 0.05 is 9.488. Our calculated chi-square value of 43.53 is much larger than the critical chi-square value. Therefore, we can reject the null hypothesis and conclude that there is a significant preference for at least one color of the coach seating redesign. Based on the count of 58, gray was clearly the preferred color among the participants.

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