Top Incorrect Problems

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2 What is the z-score for scores in the bottom 5%? a) b) c).4801 d) The score is not listed in the table.

3 A professor grades 120 research papers and reports that the average score was an 80%. What do we know about the sum of the differences of these 120 scores from their mean of 80%? a) The sum of the differences is minimal. b) It is impossible to know without knowing each of the 120 scores. c) The sum of the differences is equal to zero. d) The sum of the differences is 80%, the same as the mean.

4 A researcher measures the mean time (in seconds) it takes two groups of children to complete an activity task. She finds that Group A (M = 22 seconds) completed the task more quickly than Group B (M = 36 seconds). She then computes a weighted mean for both groups combined and calculates M W = 26. Based on the information provided, which group had a larger sample size? a) The sample size is equal in both groups. b) It is not possible to know this without knowing the sample size for each group. c) Group B d) Group A

5 Which of the following distributions has the largest variability? a) scores: 1, 2, 3, 4, and 5 b) scores: 1, 3, 6, 9, and 12 c) scores: 22, 24, 26, 28, and 30 d) scores: 2, 3, 4, 5, and 6

6 Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means? a) the fact that sample means vary minimally from the population mean b) the fact that increasing sample size will decrease standard error c) the skewed distribution rule d) the central limit theorem

7 Sample Computational Problems Compute the mean and standard deviation for the following sample of data: 11, 14, 10, 7, 12, 3

8 Sample Computational Problems Mensa International is the most well-known of the high-iq societies, unusual clubs whose only criterion for entry is that members score extremely well on an IQ test. To be considered for membership in Mensa, applicants must score in the 98th percentile on one of various IQ tests. For an IQ test normed to have a mean of 100 and a standard deviation of 15, what is the minimum score required for membership in Mensa?

9 Standard Normal Table (z-table) z Upper-Tail Probabilities

10 Sample Computational Problems Road tests of a certain compact car show a mean fuel rating of 30 miles per gallon, with a standard deviation of 4 miles per gallon. What percentage of these cars will achieve mpg ratings of a) More than 35 miles per gallon b) Less than 27 miles per gallon c) Between 27 and 35 miles per gallon

11 Standard Normal Table (z-table) z Upper-Tail Probabilities

12 Sample Computational Problems I give you a bag of M&Ms containing 2 red M&Ms and 4 blue ones. You draw two M&Ms from the bag without replacement. a) What is the probability of drawing exactly one red M&M? b) What is the probability that the second M&M drawn was blue given that the first M&M was red?

13 If we know that the probability for z > 1.5 is.067, then we can say that a) the probability of exceeding the mean by more than 1.5 standard deviations is.067. b) the probability of being more than 1.5 standard deviations away from the mean is.134. c) 86.6% of the scores are less than 1.5 standard deviations from the mean. d) all of the above

14 The population variance is a) a biased estimate. b) an estimate of the sample variance. c) calculated exactly like the sample variance. d) usually an unknown that we try to estimate.

15 I am looking down on a parking lot in which 40% of the vehicles are silver and about 25% of the vehicles are pickup trucks. To estimate that probability that the next vehicle to leave the parking lot will be a silver pickup, we first need to a) assume that the color and the type of vehicle are independent. b) assume that the color and the type of vehicle are exhaustive. c) assume that the color and the type of vehicle are mutually exclusive. d) simply multiply the two probabilities.

16 If we multiply a set of data by a constant, such as converting feet to inches, we will a) leave the mean unchanged but alter the standard deviation. b) leave the mean and variance unaffected. c) multiply the mean by the constant but leave the standard deviation unchanged. d) multiply the mean and the standard deviation by the constant.

17 A population has SS= 100 and σ 2 = 4. What is the value of Σ(x - µ) for the population? a) 25 b) 400 c) 100 d) 0

18 In a normal distribution, about how much of the distribution lies within two (2) standard deviations of the mean? a) 95% of the distribution b) 33% of the distribution c) 66% of the distribution d) 50% of the distribution

19 Sample Extra Credit Problem John s commute along Route A normally takes a mean of 38 minutes, with a standard deviation of 5 minutes. Imagine that John finds a second route to work (Route B) that takes slightly less time on average (µ = 35 minutes), but makes his commute time more variable (σ = 10 minutes). Assume that the travel times for both routes are normally distributed and that John takes Route A 55% of the time and Route B 45% percent of the time. For a randomly selected trip to work: a) Given that John takes Route B, what is the probability that the trip takes less than 45 minutes? [2.5 pts] b) What is the marginal probability that a randomly selected trip (i.e., using either Route A or Route B) takes more than 45 minutes? [5 pts] c) Assuming that John s goal is to make it to work in less than 45 minutes as often as possible, which route should he use and why? [2.5 pts]

20 Standard Normal Table (z-table) z Upper-Tail Probabilities