Advanced Business Statistics: Key Concepts & Sample Questions

MGSC 372: Advanced Business Statistics Name: Section (circle one): 11:30am 4pm Have you taken the Introduction to Finance core course? (circle one): Completed Currently enrolled No In which semester did you take MGCR 271: Business Stats? (circle one): F23 W23 F22 W22 F21 W21 F20 Other 1. The scores on a standardized test follow a normal distribution with mean 400 and standard deviation 100. Approximately what percentage of students scored above 500? A) 68% B) 34% C) 16% D) 5% 2. In a survey of 200 Montreal tech startups, it is found that the distribution of the number of employees has the following box plot: Min: 23 Q1: 31.5 Q2: 43.5 Q3: 67.5 Max: 92 True or False: The number of companies with between 31.5 and 43.5 employees is smaller than the number of companies with between 43.5 and 67.5 employees. True False

3. Which of the following statements about the following set of data is correct? 4 12 6 18 22 7 100 6 8 A) The mean is larger than the median due to the presence of a large outlier that pulls the average up. B) The mean is smaller than the median due to the presence of many single-digit values that pull the average down. 4. True or False: the Central Limit Theorem says that if a large sample is drawn from any population and a quantitative variable is measured for each individual in the sample, the histogram of this variable will look approximately normal. True False 5. A basketball player makes 80% of her free throws. If she takes 5 free throws in a game, which of the following expressions represents the probability that she misses at least one? (Assume that the outcomes of the free throws are independent.) A) 0 . 8 5 B) 1 − 0 . 8 5 C) 0 . 2 5 D) 1 − 0 . 2 5

6. A Covid rapid test has a false positive rate of 1% and a false negative rate of 10%. If 1000 people take this test and 3% of them actually have Covid, which of the following is most likely? A) There will be more false positive tests than false negative tests. B) There will be more false negative tests than false positive tests. C) There will be approximately the same number of false positive and false negative tests. The next two questions refer to the following information. For their final project, a team of MGCR 271 students visits 30 coffee shops. For each shop, they record the price of a latte (in dollars) and the distance from McGill (in km). They run a simple regression to see if the distance from McGill has an effect on the price of a latte, and the resulting regression equation is Price = 6 . 2 − 0 . 2 ∗ Distance 7. True of False: According to this regression equation, lattes tend to get more ex- pensive as you get closer to McGill. True False

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8. In the regression described in the previous question, the P-value for the slope is 0.35. This P-value indicates which of the following? A) The observed correlation between price and distance is statistically significant— if the price of a latte is unrelated to the distance from McGill, it is unlikely that such a strong correlation would have been observed. B) The observed correlation between price and distance is NOT statistically significant— it may very well just be due to chance. The next two questions refer to the following information. Delphine wants to test a company’s claim that their boxes of cherry tomatoes contain an average of 37 tomatoes. She collects a sample of boxes and counts the number of tomatoes in each box. Based on her sample, she calculates a 95% confidence interval for the true average number per box to be [36,42]. 9. What is the average number of tomatoes per box in Delphine’s sample? A) can’t be determined without knowing the sample size B) can’t be determined without knowing the sample standard deviation C) 37 D) 39 10. Delphine uses her sample to test the null hypothesis that the true average is 37 against the two-sided alternative hypothesis. The P-value for this hypothesis test is A) less than 0.05 B) greater than 0.05

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