PSU STAT 200 MASTERY QUIZ 1
PSU STAT 200 MASTERY QUIZ 1
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Date Created: 11/14/15
PSU STAT 200 MASTERY QUIZ 1 1. Which statistic may be used to summarize a set of categorical data? A) Percent in each category B) Median C) Mean Feedback: Mean and median are statistics that describe a quantitative data set. The percent that falls in each category can be used to describe a categorical data set. Points Earned: 0.0/1.0 Correct Answer(s): A 2. In order to employ the Empirical Rule which one of the following is true? A) The data needs to be Empirical. B) The data needs to be bell shaped C) The data needs to be normal D) The Empirical Rule works for any data set. Feedback: The data needs to be bell shaped. Normal is a specific type of bell shaped distribution, but is not necessary to employ the Empirical Rule. Points Earned: 1.0/1.0 B Correct Answer(s): 3. A study was done at Penn State to determine the attitudes students have regarding students carrying guns on campus. The study design involved randomly selecting 50 students from each class standing: Freshman, Sophomore, Junior, Senior, and Graduate. The design BEST describes which sampling method? A) Stratified B) Simple Random C) Cluster D) Convenience Feedback: Randomly selecting from each class standing, or strata, would be an example of stratified random sampling. Points Earned: 1.0/1.0 Correct Answer(s): A 4. When graphing categorical data, which of the following graphs would be MOST appropriate? A) Box plot B) Pie Chart C) Histogram D) Stem and Leaf Feedback: Except for the pie chart, all other graphs are for quantitative data. Points Earned: 1.0/1.0 Correct Answer(s): B 5. What observed height would have a zscore of zero? A) 65 B) 69 C) 73 D) 0 Feedback: For a zscore of 0 we would find the observed height using the equation: observed equals z score times SD plus mean. A zscore 0 times 4 would be 0, and adding this to a mean of 69 would simply be 69. Or, if you recall that zscores represent the number of standard deviations an observed score is from the mean then a zscore of 0 would mean the observation was zero standard deviations from the mean thus the observed value would be the mean. Points Earned: 1.0/1.0 Correct Answer(s): B 6. Approximately what percent of male heights are between 65 inches and 73 inches? A) 99.7 B) 95 C) 68 D) 50 Feedback: Since bellshaped then approximately 68% of the heights would be between one standard deviation of the mean or 65 and 73 inches. Points Earned: 0.0/1.0 Correct Answer(s): C 7. The shape of the above frequency distribution reflects which of the following shapes? A) Skewed right or positively skewed B) Skewed left or negatively skewed C) Symmetrical Feedback: With the data being “pulled” to the right (i.e. the data has a tail that stretches to the right) this would reflect a right skew or positive skew. Points Earned: 1.0/1.0 Correct Answer(s): A 8. A magazine publisher asks readers to log onto their website and vote on a topic. The website allows visitors to select one of two choices and submit a vote. The results of the poll are reported in the next issue of the magazine. The population to which the results of these polls can be extended is A) all readers who have voted in any of the polls. B) all visitors to the website. C) only readers who voted in that specific poll. D) all readers of the magazine. Feedback: Without a statistical sampling method the results can only extend to those readers who voted in that specific poll Points Earned: 1.0/1.0 Correct Answer(s): C 9. Which one of the following statements is true? A) Increasing the sample size of a survey increases response bias. B) Increasing the sample size of a survey decreases response bias. C) Increasing the sample size of a survey increases the margin of error. D) Increasing the sample size of a survey decreases the margin of error. Feedback: Consider the equation for margin of error; it involves dividing by the sample size n. By theory, then, as n would increase the margin of error would decrease. Also, the idea of confidence intervals is to estimate the true parameter value. So the larger the sample size the close your size of the sample approaches the population size thus the error should decrease. Sample size has no effect on response bias. For example, even if a professor asked more and more students whether they ever cheated on an exam, response bias would most likely exist regardless of how many students were sampled. Points Earned: 1.0/1.0 D Correct Answer(s): 10. The five number summary for a Stat200 exam is given above. What would the lower fence value be in order to check for outliers? A) 5 B) 30 C) 0 D) 20 Feedback: We would find the lower fence by Q1 minus 1.5 times the IQR. With the IQR found by Q3 minus Q1 or 80 minus 50 equaling 30, the lower fence is 50 minus 1.5 times 30 which is 50 minus 45 coming to a lower fence value of 5. Points Earned: 0.0/1.0 Correct Answer(s): A 11. The five number summary for a Stat200 exam is given above. What is the interquartile range (IQR)? A) 45 B) 25 C) 30 D) negative 30 E) 75 Feedback: The IQR is found by Q3 minus Q1; IQR is then 80 minus 50 or 30. Points Earned: 0.0/1.0 Correct Answer(s): C 12. The five number summary for a Stat200 exam is given above. Which of the following ranges contains the top 25% of the exam scores? A) 75 to 100 B) 75 to 80 C) 0 to 50 D) 80 to 100 Feedback: The top 50% of observations would be from Q3 to the max of from 80 to 100 to Q3 or 55 to 80. Points Earned: 0.0/1.0 Correct Answer(s): D 13. Suppose a car manufacturing company wanted to gather data about what color of cars people prefer. They instructed you to walk around the city and take note of the color of cars that you see. What data collection method are you using? A) Observational Study B) Survey C) Experiment D) Published Data Feedback: Since you are not asking anyone any questions but simply observing, this would be an observational study. Points Earned: 1.0/1.0 Correct Answer(s): A 14. What is the probability that one person of a randomly chosen couple has type A blood and the other has type O? A) 0.70 B) 0.12 C) 0.20 D) 0.24 Feedback: The possible outcomes are Husband has A and Wife has O, or Husband has O and Wife has A. We answer this question by P(A and O) plus P(O and A) or by twice P(A and O). Since the problem states that blood types are independent, P(A and O) = P(A)P(O) = 0.30*0.40 = 0.12 Doubling this gives us the correct answer of 0.24 Points Earned: 0.0/1.0 Correct Answer(s): D 15. There are 15 students in a class. Every day the instructor randomly calls on six different students, and a student cannot be called on twice in the same class. Today the instructor has already called on five students, and Tony has not yet been called. Given this information, what’s the probability that Tony will be the sixth student called? A) 1/10 B) 1/12 C) 1/2 D) 1/3 Feedback: Starting with 15 students and selecting without replacement the first 5 students, there are 10 students left from which one would be picked: 1/10. Points Earned: 1.0/1.0 Correct Answer(s): A 16. A sixsided die is made that has four green sides and two red sides, all equally likely to land face up when the die is tossed. The die is tossed three times. Which of these sequences (in the order shown) has the highest probability? A) They are all equally likely B) Green, Green, Green C) Green, Green, Red D) Green, Red, Red Feedback: Since Green is more likely then getting all Green is most likel outcome Points Earned: 1.0/1.0 Correct Answer(s): B 17. Given Company A offers you a job, what is the probability that Company B will also offer you a job? A) 1.10 B) 0.30 C) 0.70 D) 0.80 E) 0.10 Feedback: The question asks you to find P(B|A) = P(A and B)/P(A) = (0.40)/(0.50) = 0.80 Points Earned: 0.0/1.0 Correct Answer(s): D 18. The sample mean is an estimate of: A) The average value for people NOT in the population B) The average value in the sample C) The true population mean Feedback: The sample mean is an estimate of the true population mean. It is, however, an exact measurement of the average value in the sample since the sample data is what is used to calculate the sample mean. Points Earned: 1.0/1.0 Correct Answer(s): C 19. The above probability distribution represents classes missed so far this week by students in a population. What is the expected value of X = number of misses? That is, find E(X). A) 0.7 B) 1.5 C) 6 D) 0 Feedback: Using the formula of multiplying each observation times its respective probability and then summing these results produces E(X) = 0*0.6 + 1*0.2 + 2*0.1 + 3*0.1 = 0.7 Points Earned: 0.0/1.0 Correct Answer(s): A 20. A student does not study for a 10 question multiple choice quiz, with five answer choices for each question, so he randomly guesses an answer for every question. Which choice below describes how to find the probability that this student gets exactly 7 questions correct? A) Find cumulative probability for 7 successes for a binomial variable with n = 10 and p = 1/5. B) Find probability of 7 successes for a binomial variable with n = 10 and p = 7/10 C) Find cumulative probability for 7 successes for a binomial variable with n = 10 and p = 7/10. D) Find probability of 7 successes for a binomial variable with n = 10 and p = 1/5 Feedback: Cumulative probability implies less than or equal to and in this problem you are asked to find exactly. Thus both cumulative statements are incorrect. With 5 questions, the probability of success is 1/5. Points Earned: 0.0/1.0 Correct Answer(s): D 21. A summary measure calculated from the sample is called a(n): A) outlier B) statistic C) parameter Feedback: Sample measures are statistics; population measures are parameters Points Earned: 1.0/1.0 Correct Answer(s): B 22. The probability of winning on lottery ticket is 0.2. Several lottery tickets are selected at random where X = winning on a ticket. If we want to find P(X < 2) can we apply binomial methods? A) No, because each trial is not independent. B) No, because the number of trials are not fixed. C) Yes, because all of the binomial conditions are satisfied D) Not, because the probability of success is not constant for each trial Feedback: The number of trials is not fixed. Several is not a fixed value. Points Earned: 0.0/1.0 B Correct Answer(s): 23. Use the Standard Normal Table to find the following probability for X = Student Heights for which the mean is 66 inches and the standard deviation is 2 inches: P(66 < X < 69) A) – 0.3531 B) 0.4332 C) 0.3531 D) – 0.4332 Feedback: Find the two zscores and the cumulative probability for each: zscore of (66 – 66)/2 = 0 and zscore by (69 – 66)/2 = 1.50 with respective cumulative probabilities of 0.5000 and 0.9332 from which you take the difference to get 0.4332 Points Earned: 0.0/1.0 Correct Answer(s): B 24. Use the Standard Normal Table to find the following probability for X = Student Heights for which the mean is 66 inches and the standard deviation is 2 inches: P(X > 69) A) 0.1469 B) 0.9332 C) 0.8531 D) – 0.1469 E) 0.0668 F) – 0.0668 Feedback: Find the zscore by (69 – 66)/2 = 1.50 and then from the Standard Normal Table find the cumulative probability for 1.50 which is 0.9332. Since we want to find greater than 1.50 we subtract this cumulative probability from 1 and get P(X > 69) = 0.0668 Points Earned: 0.0/1.0 Correct Answer(s): E 25. Some managers of companies use employee rankings to reward the best and let go of the worst. Suppose the distribution of rankings of employees at a large company is normal with a mean of 65 points and a standard deviation of 6 points. What proportion of employees has a ranking between 59 and 71? A) 0.8413 B) 0.1587 C) – 0.6826 D) 0.6826 E) – 0.1587 Feedback: Find the two zscores and the cumulative probability for each: zscore of (59 – 65)/6 = – 1.00 and zscore by (71 – 65)/6 = 1.00 with respective cumulative probabilities of 0.1587 and 0.8413 from which you take the difference to get 0.6826 Points Earned: 0.0/1.0 Correct Answer(s): D 26. Which of the following refers to when a large enough sample is taken the mean of the sample distribution can be assumed to follow approximately a normal distribution? A) Normal distribution B) Binomial distribution C) Central Limit Theorem D) Empirical Rule E) Law of large numbers Feedback: The central limit theorem is a powerful tool in statistics in such a case. This theorem allows us to assume that the sample mean of the data approximately follows a normal distribution regardless of the population distribution when the sample size is large enough (i.e. n at least 30). Points Earned: 1.0/1.0 Correct Answer(s): C 27. From a random sample of 20 women from a women’s only health club, 60%, or 12, stated that they wished the club would stay open longer. Which of the following best defines what this 60% represents? A) population B) sample C) statistic D) parameter Feedback: Because this value came from a sample the 60% defines a statistic. Points Earned: 1.0/1.0 Correct Answer(s): C 28. The name of a manufacturer of CD players. A) Categorical B) Quantitative Feedback: The name of a manufacturer of CD players is categorical since it cannot be counted. Points Earned: 1.0/1.0 Correct Answer(s): A 29. The flavor of ice cream a person prefers to eat the most (chocolate, vanilla, etc.). A) Categorical B) Quantitative Feedback: The flavor of ice cream a person prefers is categorical since we do not count it. Points Earned: 1.0/1.0 Correct Answer(s): A 30. If you took a random sample of 36 university women from this population, there would be a 95% chance that the average weight would be between: A) 133 and 137 pounds. B) 119 and 151 pounds. C) 131 and 139 pounds. D) 123 and 147 pounds. E) 129 and 141 pounds. Feedback: We know the standard error is 12/sqrt(36) = 2. Using the empirical rule, we know that 95% of the observations lie within +/ 2 standard deviation of the mean. So, there is a 95% chance that the average weight will be between 135 (2(2))and 135 + (2(2)), 131 and 139 pounds. Points Earned: 1.0/1.0 Correct Answer(s): C
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