[기출문제] 서강대 통계학개론 (기초통계학) 2020-2 기말 기출문제 (정답 포함)

서강대 통계학개론 (기초통계학) 2020-2 기말 기출문제 (정답 포함)

 

 

 

1. 시험 정보

 

학교/과목	서강대 통계학개론 (기초통계학)
시험명	2020-2 기말
교수명	-
문항수/형식	서술형 2문제 / 풀이형 5문제
정답/해설	✅ 있음
파일형식	docx

 

 

 

2. 출제 범위 & 키워드

 

통계학(가설검정·회귀분석·분산분석) 종합 응용

 

 

📚 키워드

 

 

 

 

 

3. 기출 미리보기

 

 

Q1-1. Fill in the blank. : A directional alternative hypothesis is more (___________) than a non-directional one in detecting a difference, if there really exists a difference in the data.

 

 

 

4. 자료 보기

 

 

[기출 문제] 

 

*** Show all your problem-solving processes on these sheets to receive full points. *** Problem 1 Answer the following questions: Q1-1. Fill in the blank. : A directional alternative hypothesis is more (___________) than a non-directional one in detecting a difference, if there really exists a difference in the data. Q1-2. Why do we call “analysis of variance”, not “analysis of mean”, for testing the means of more than two groups in the ANOVA test? Problem 2 Nike Co. wants to estimate the sales revenue of its stores to determine which stores to be shut down. They collected a sample of 25 stores with the following variables:  Y = the Nike store’s sales revenue (in million dollars);  X1 = the Nike store’s size (in square foot);  X2 = the Nike store’s advertising expenditure (in million dollars);  X3 = the Nike store’s location: “S” for Seoul, “C” for cities, and “T” for towns;  X4 = the competitor’s promotional expenditure (in million dollars); You are given the following two computer outputs: Output – I Regression Statistics Multiple R 0.3914 R Square 0.1532 Adjusted R Square 0.1164 Standard Error 100.6035 Observations 25 ANOVA 　 df SS MS F P-value Regression 1 42130.64 42130.65 4.1626 0.05296 Residual 23 232784.71 10121.07 Total 24 274915.36 　 　 　 　 Coefficients Standard Error t Stat P-value Intercept 91.67 100.14 0.915 0.3694 X2 7.29 3.57 2.040 0.0529 Output – II Regression Statistics Multiple R 0.5141 R Square ? Adjusted R Square 0.2324 Standard Error 93.772 Observations 25 ANOVA 　 df SS MS F P-value Regression 1 72670.9 72670.9 8.2644 0.0085 Residual 23 202244.5 8793.237 Total 24 274915.4 　 　 　 　 Coefficients Standard Error t Stat P-value 　 Intercept 407.78 44.47 9.168 3.83E-09 X4 -11.47 3.99 -2.874 0.0085 　 Output – III Groups Count Sum Average Variance C 10 3141 314.1 3819.211 S 7 2580 368.5714 4775.619 T 8 1575 196.875 13367.55 ANOVA Source of Variation SS df MS F P-value Between Groups 118315.9 2 59157.94 8.3108 0.0020 Within Groups 156599.5 22 7118.159 Total 274915.4 24 　 　 　 Answer the following questions. 1. Can we be reasonably confident that Nike’s advertising expenditure has a positive effect on the Nike store’s sales revenue ( = 5%)? (1) Ho and Ha can be set up in two different ways. State both cases. Ho (symbolically): (in words): Ha (symbolically): (in words): Or alternatively, Ho (symbolically): (in words): Ha (symbolically): (in words): (2) Define test, show test statistic, p-value, and alpha in the diagram: (3) conclusion: 2. In the above model (Question 1), find and interpret the coefficient of determination? 3. Interpret the meaning of standard error of estimate in the problem. 4. Predict the sales revenue if a store spends 100 million dollars for advertising. 5. Can we be reasonably confident that the store’s sales revenue differs by the store’s location ( = 5%)? (1) Ho (symbolically): (in words): Ha (symbolically): (in words): (2) Define test, show test statistic, p-value, and alpha in the diagram: (3) conclusion:

 

 

[정답]

 

Problem 1 (1) Ho: β2 ≤ 0 (in words): Advertising has no positive effect (zero or negative effect) on sales revenue. Ha: β2 > 0 (in words): Advertising has a positive effect on sales revenue. Or alternatively, Ho: β2 = 0 (in words): Advertising has no effect on sales revenue. Ha: β2 ≠ 0 (in words): Advertising affects sales revenue. (2) t = 2.040 (df = 23), α = 0.05 Two-tailed p-value = 0.0529 One-tailed p-value (for β2 > 0) ≈ 0.0529 / 2 = 0.02645 (3) Using the one-tailed test: p ≈ 0.02645 < 0.05, reject Ho. We can be reasonably confident that Nike’s advertising expenditure has a positive effect on sales revenue. Problem 2 R² = 0.1532 Interpretation: About 15.32% of the variation in sales revenue is explained by advertising expenditure (X2) in this model. Problem 3 Standard Error = 100.6035 (million dollars) Interpretation: The typical prediction error (typical distance between actual sales and predicted sales) is about 100.6 million dollars. Problem 4 Ŷ = 91.67 + 7.29X2 If X2 = 100, then Ŷ = 91.67 + 7.29(100) = 820.67 Predicted sales revenue: 820.67 million dollars Problem 5 (1) Ho: μC = μS = μT (in words): Mean sales revenue is the same across Seoul, cities, and towns. Ha: Not all means are equal (at least one differs) (in words): Mean sales revenue differs by location. (2) F = 8.3108, p-value = 0.0020, α = 0.05 (3) Since p = 0.0020 < 0.05, reject Ho. We can be reasonably confident that sales revenue differs by store location.

 

 

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