Mock Exam - mock exam 17/18
Statistics II for IB (EBB682B05)
Rijksuniversiteit Groningen
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Statistics II for IB (2017/2018) ——————————————————————————————— Mock Exam ——————————————————————— Solutions will be discussed on the last lecture only. Please prepare the Mock Exam beforehand. Name: Student number: • Please indicate clearly your name and student number. • This exam accounts for 30% of your grade, the total points you can obtain is 30. • There are 10 multiple choice questions for 1 point and 10 for 2 points. Please mark your answers on the multiple-choice form. • Unless it is specified otherwise, assume a 5% significance level for all questions. • Note that the outputs from SPSS use a decimal comma instead of a decimal point. Good luck! 1. (1 point) Which statement is correct? The higher the significance level... A. the higher the absolute value of the critical value(s) will be, which makes it more likely to reject the null hypothesis. B. the higher the absolute value of the critical value(s) will be, which makes it less likely to reject the null hypothesis. C. the lower the absolute value of the critical value(s) will be, which makes it more likely to reject the null hypothesis. D. the lower the absolute value of the critical value(s) will be, which makes it less likely to reject the null hypothesis. 2. (1 point) Assume the usual notation: n is the sample size, k is the number of explanatory variables, r is the number of rows and c is the number of columns in a crosstab. Which of the following statements is FALSE? A. The degree of freedom of a χ2 -test can be n − 1. B. The degree of freedom of a χ2 -test can be k − 1. C. The degree of freedom of a χ2 -test can be (r − 1)(c − 1). D. None of the above statements is true. 3. (1 point) Calculate the Jarque-Bera Test for Normality for the variable “Labor force, female” based on the following output from SPSS (n = 185): A. The test value (JB=88) exceeds the critical value both for 5% and for 10%, hence normality can be rejected. B. The test value (JB=82) exceeds the critical value both for 5% and for 10%, hence normality can be rejected. C. The test value (JB=88) exceeds the critical value both for 5% and for 10%, hence normality can’t be rejected. D. The test value (JB=82) exceeds the critical value both for 5% and for 10%, hence normality can’t be rejected. 1 9. (1 point) The correlograms below present the ACF and PACF of a company’s earnings per share per quarter. How many lags should be included in an AR(p) process? A. None B. 1 C. 2 D. As many as possible 10. (1 point) Consider the previous question. Which time-series component is most visible from the correlograms? A. The trend component B. The cyclical component C. The seasonal component D. The irregular component 11. (2 points) A statistican would like to test whether a coin is fair. He conducts a series of experiments: he tosses the coin 5 times and writes down the number of heads. He does this 100 times. The results are summarized in the following table: Number of heads 0 1 2 3 4 5 Frequency 4 14 32 30 17 3 Conduct a test with 10% significance level to determine whether the Binomial distribution can be assumed. Hint: calculate or look up the probabilities of tossing 0, 1, etc. heads first. 3 A. The p-value is between 0 and 0, therefore the null hypothesis should be rejected: the coin appears to be unfair. B. The p-value is between 0 and 0, therefore the null hypothesis should be rejected: the coin appears to be unfair. C. The p-value is between 0 and 0, therefore the null hypothesis should be rejected: the coin appears to be unfair. D. The p-value is above 0, therefore the null hypothesis can’t be rejected: the coin appears to be fair. 12. (2 points) A study was conducted to determine whether the use of seat belts in vehicles depends on ethnic status in Detroit. A sample of 1000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) ethnic status (African American or non-African American) and (2) set belt usage (worn or not worn) during the accident. The data are shown in the table below. Seat Belts Worn Not worn African American 83 337 Non-African American 200 380 Does the use of seat belts in vehicles depends on ethnic status in Detroit? A. Since 0 < χ2 < 10 and χ2 < χ21,0 , we do not reject H0 and conclude that use of seat belts in vehicles does not depend on ethnic status in Detroit. B. Since 0 < χ2 < 10 and χ2 > χ21,0 , we reject H0 and conclude that use of seat belts in vehicles depends on ethnic status in Detroit. C. Since 10 < χ2 < 20 and χ2 > χ21,0 , we reject H0 and conclude that use of seat belts in vehicles depends on ethnic status in Detroit. D. Since 20 < χ2 < 30 and χ2 > χ21,0 , we reject H0 and conclude that use of seat belts in vehicles depends on ethnic status in Detroit. 13. (2 points) Sixteen first year students were grouped into eight pairs in such a way that the two members of any pair were as similar as possible in academic and social backgrounds. The major difference within pairs was that one student was Dutch and the other was international. At the end of their studies grade point averages of these students were recorded, yielding the results shown in the table. We want to test the null hypothesis that the differences are centered at 0. Use a significance level of α = 5%. Pair A B C D E F G H Dutch 7 7 6 7 8 6 6 7 Which of the following statements is TRUE? 4 International 6 7 6 7 8 6 6 7 15. (2 points) Consider the previous question. Which of the following models will result in the highest R2 value in the estimated model? A. type = β0 + β1 · price + β2 · horsepow + β3 · width + β4 · length + B. price = β0 + β1 · type + β2 · horsepow + β3 · width + β4 · length + C. horsepow = β0 + β1 · type + β2 · price + β3 · width + β4 · length + D. length = β0 + β1 · type + β2 · price + β3 · horsepow + β4 · width + 16. (2 points) Consider the two questions before. Which of the following statements is TRUE? A. Based on the individual t-tests we can conclude that the R2 of the estimated model is not different from zero. B. Based on the overall F-test we can conclude that the R2 of the estimated model is not different from zero. C. Based on the individual t-tests we can conclude that the R2 of the estimated model is significantly different from zero. D. Based on the overall F-test we can conclude that the R2 of the estimated model is significantly different from zero. 17. (2 points) An analysis of variance table is displayed below with missing values, denoted by asterisks. What does the value of the test statistic F equal to? A. 1 B. 1 C. 2 D. 2 18. (2 points) An accusation has been made regarding the grade distribution in a course. According to students the mean grades are different for different tutorial teachers and whether the class takes place in the morning or the afternoon. The Board of Examiners decides to look into the accusation and therefore creates the following two-way ANOVA table: 6 Which conclusions seem to be valid? A. The mean grades differ with different tutorial teachers but do not exhibit any difference across time. B. The mean grades differ with different times but do not exhibit any difference across tutorial teachers. C. The mean grades can be considered equal for different tutorial teachers and different times, but there is a significant interaction effect. D. Neither the tutorial teachers or time, or their interactions seem to influence the mean grades. 19. (2 points) Consider the following time series about the population of a city: Year Population (in thousand) 2011 272 2012 275 2013 278 2014 276 2015 278 Which one is the centered 4-point moving average for 2013? A. 275 B. 275 C. 276 D. 277 20. (2 points) The table below is the data set of the Shiller Real Home Price Index for the years 1894-1898. Year Price Index 1894 123 1895 117 1896 100 1897 106 1898 110 Use a smoothing constant of α = 0 to determine the forecast for the year 1896 using simple exponential smoothing. A. The forecast is 103. B. The forecast is 104. C. The forecast is 106. D. The forecast is 109. 7
Mock Exam - mock exam 17/18
Vak: Statistics II for IB (EBB682B05)
Universiteit: Rijksuniversiteit Groningen
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