# Statistics - 1 QUESTION 1 License records in a count reveal...

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1 QUESTION # 1 License records in a count reveal that 15% of cars are subcompacts (1), 25% are compacts (2), 40% are midsize (3), and the rest are an assortment of other styles and models (4). A random sample of accidents involving cars licensed in the county was drawn. The type of car was recorded using the codes in parentheses. Can we infer that certain sizes of cars are involved in a higher than expected percentage of accidents? (Dataset XR 16-13.sav) Step 1: Hypothesis Development H 0 : p 1 = .15, p 2 = .25, p 3 = .40, p 4 = .20 H 1 : At least one p i is not equal to its specified value. Step 2: Significance Level α = 0.05 Step 3: Test Statistics The sample selected here is composed of accidents involving cars licensed in the county. The data are nominal because accidents can take place in four choices of cars – subcompacts, compacts, midsize, or others. As we’re interested in the proportions of all four categories, this experiment is a multinomial experiment, and the test statistic to be used is “chi-square test for goodness of fit”. Step 4: Assumption of Minimum Expected Cell Frequency In the table labelled “Chi-Square Tests Statistics”, footnote indicates that ‘0 cells (.0%) have expected count less than 5. The minimum expected cell frequency is 29.6’. So, data mets the assumption of minimum expected cell frequency. Step 5: Test Results From the table given below, the chi-square value is not significant at 5% level (χ 2 (3) = 6.000, asymp. sig. (2-sided) = .112). Hence, the percentage of all sizes of cars is significantly equal to its expected value. Therefore, we can conclude that certain sizes of cases are not

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2 significantly involved in a higher than expected percentage of accidents. Test Statistics types of car Chi-Square 6.000 a df 3 Asymp. Sig. .112 a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 29.6. Step 6: Conclusion The residual value in table labelled “descriptive statistics” also indicated that half of the cars have a positive residual value and half of the cars, including an assortment of other styles and models have a negative residual value. Statistically, the descriptive statistics support the test statistic result that certain sizes of cars are not involved in a higher than expected percentage of accidents. types of car Observed N Expected N Residual subcompacts 36 29.5 6.5 compacts 58 49.2 8.8 midsize 74 78.8 -4.8 others 29 39.4 -10.4 Total 197
3 QUESTION # 2 To determine whether commericals viewed during the happy television programs are more effective than those viewed during sad television programs, a study was conducted in which a random sample of students viewed as upbeat segment from “Real People” with commercials, while another sample of students viewed a very sad segment from “Sixty Minutes” with commercials. The students were then asked what they were thinking during the final commercial. From their responses, they were categorized as thinking primarily about the commercial (1), thinking primarily about the program (2), or thinking about both (3). The results were stored in file Xr 16-25. (Column 1 lists the program: 1 = “Real People” and 2 = “Sixty Minutes”; column 2 lists the responses.) Do

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• Spring '16
• Statistics, Statistical hypothesis testing, α, home runs

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