Stats Exam II

Below are a sample of two variables, X and Y. Calculate the correlation coefficient for these variables. Round to the nearest hundredth if necessary. x y 71.36 135.39 76.99 191.29 62.42 193.79 72.46 84.01 91.72 190.61

.21

Below are a sample of two variables, X and Y. Calculate the covariance for these variables. Round to the nearest hundredth if necessary. x y 1862.83 420.36 2021.06 422.28 1961.55 541.41 2006.02 573.43 2121.97 748.74

9892.35 Correlation Coefficient = Covariance/ (SDX)(SDY)

If P(A | B) = 0.40 and P(B) = 0.30, find P(A∩B). Select one: A. .525 B. .120 C. .571 D. .171

B. 120 P(A|B) = P(AUB)/P(B)

The number of unique orders in which five items (A, B, C, D, E) can be arranged is: Select one: A. 5. B. 120. C. 24. D. 840.

B. 120. -Apply rules of counting: 5 × 4 × 3 × 2 × 1 = 120.

Oxnard Casualty wants to ensure that their e-mail server has 99.98 percent reliability. They will use several independent servers in parallel, each of which is 95 percent reliable. What is the smallest number of independent file servers that will accomplish the goal? Select one: A. 4 B. 3 C. 1 D. 2

B. 3 - 1 - P(F1∩F2∩F3) = 1 - (.05) (.05) (.05) = 1 - .000125 = .999875, so 3 servers will do.

How do you find a 70th percentile of a data set?

Order the data set in chronological order L(70)= 70/100 * (n+1) -This gives you the placement of the number. if decimal, take the average of the two numbers surrounding it.

If P(A∩B) = 0.50, can P(A) = 0.20? Select one: A. Only if P(B∩A) = 0.60 B. If P(A) = 0.20, then P(A∩B) cannot equal 0.50. C. Not unless P(B) = 0.30 D. Only if P(A | B) = 0.10

B. If P(A) = 0.20, then P(A∩B) cannot equal 0.50. -The given information contains a contradiction, because P(A∩B) cannot exceed P(A).

John scored 35 on Prof. Johnson's exam (Q1 = 70 and Q3 = 80). Based on the fences, which is correct? Select one: A. John is unusual but not an outlier. B. John is an outlier. C. John is in the 30th percentile. D. John is neither unusual nor an outlier.

B. John is an outlier. -The lower inner fence is 70 - 1.5(80 - 70) = 55 so John is an outlier. Actually, John is an extreme outlier because the lower outer fence is 70 - 3.0(80 - 70) = 40.

In a certain city, 5 percent of all drivers have expired licenses, 10 percent have an unpaid parking ticket, and 1 percent have both an expired license and an unpaid parking ticket. Are these events independent? Select one: A. Can't tell from given information B. No C. Yes

B. No -For independence we would require P(A)P(B) = P(A∩B).

Which two statistics offer robust measures of center when outliers are present? Select one: A. Midrange and geometric mean. B. Mean and mode. C. Median and trimmed mean. D. Variance and standard deviation.

C. Median and trimmed mean. -Extremes are excluded from the trimmed mean and do not affect the median.

The probability that event A occurs, given that event B has occurred, is an example of: Select one: A. more than one of the above. B. a marginal probability. C. a conditional probability. D. a joint probability.

C. a conditional probability. -CorrectReview definition of conditional probability.

Regarding the rules of probability, which of the following statements is correct? Select one: A. If A and B are independent events, then P(B) = P(A)P(B). B. The sum of two mutually exclusive events is one. C. If event A occurs, then its complement will also occur. D. The probability of A and its complement will sum to one.

D. The probability of A and its complement will sum to one.

As a measure of variability, compared to the range, an advantage of the standard deviation is: Select one: A. describing the distance between the highest and lowest values. B. being calculated easily through the use of a formula. C. considering only the data values in the middle of the data array. D. considering all data values.

D. considering all data values. - The range is easy to calculate but utilizes only two data values, which may be unusual.

Events A and B are mutually exclusive when: Select one: A. they are independent events. B. P(A)P(B) = P(A | B) C. P(A)P(B) = 0 D. their joint probability is zero.

D. their joint probability is zero.

Two events are complementary (i.e., they are complements) if: Select one: A. they are independent events with equal probabilities. B. the joint probability of the two events equals one. C. the sum of their probabilities equals one. D. they are disjoint and their probabilities sum to one.

D. they are disjoint and their probabilities sum to one.

Below is a sample of the number of students arrested for public intoxication at randomly selected PAC12 Universities in 2017. What is the variance of these arrests? If necessary, round to the nearest hundredth. 790 733 217 355 950

95649.5

The value of 6C2 is: Select one: A. 15. B. 720. C. 30. D. 12.

A. 15 -Apply the formula for combinations. n! / r! (n-r)!

The following are a random sample of scores from a Likert Scale. Last semester, students were asked to respond to the statement "Dr. Callahan was an effective teacher." The numbers, ranging 1 to 5, represent student attitudes towards this statement, with 5 being the highest. What is the median of these scores? If necessary, round to the nearest hundredth. 1 5 2 2 1 3 1 1 1 2

1.5

Below is a sample of the number of students arrested for public intoxication at randomly selected PAC12 Universities in 2017. What is the standard deviation of these arrests? If necessary, round to the nearest hundredth. 790 733 217 355 950

309.27

Below is a random sample of exam 1 test scores for Chris Giguere's section of ECO2100. What is the mean of these test scores? Round to the nearest hundredth. 53.14 66.73 67.30 51.86 74.79 26.51 41.17 30.55 41.34 70.83

52.42

For U.S. adult males, the mean height is 178 cm with a standard deviation of 8 cm and the mean weight is 84 kg with a standard deviation of 8 kg. Elmer is 170 cm tall and weighs 70 kg. It is most nearly correct to say that: Select one: A. Elmer is heavier than he is tall. B. Elmer's weight is more unusual than his height. C. Height and weight have the same degree of variation. D. Height has more variation than weight.

B. Elmer's weight is more unusual than his height. -Convert Elmer's height and weight to z-scores. For Elmer's weight, z = (x - μ)/σ = (70 - 84)/8 = -1.75, while for Elmer's height, z = (x - μ)/σ = (170 - 178)/8 = -1.00. Therefore, Elmer is farther from the mean weight than from the mean height.

If two events are collectively exhaustive, what is the probability that one or the other will occur? Select one: A. 0.50 B. Can't tell from given information C. 1.00 D. 0.00

C. 1.00 -Review definition of probabilities (collectively exhaustive covers all the possibilities).

The quartiles of a distribution are most clearly revealed in which display? Select one: A. Scatter plot B. Dot plot C. Box plot D. Histogram

C. Box Plot -The histogram, scatter plot, or dot plot will not directly show quartiles.

Which statement is false? Select one: A. If P(A) = .05, then the odds against event A's occurrence are 19 to 1. B. The number of permutations of five things taken two at a time is 20. C. If A and B are mutually exclusive events, then P(A or B) = 0.

C. If A and B are mutually exclusive events, then P(A or B) = 0.

Which is a correct statement concerning the median? Select one: A. The median is halfway between Q1 and Q3 on a box plot. B. The median is an observed data value in any data set. C. In a left-skewed distribution, we expect that the median will exceed the mean. D. The sum of the deviations around the median is zero.

C. In a left-skewed distribution, we expect that the median will exceed the mean. -The mean is pulled down in left-skewed data, but deviations around it sum to zero in any data set. The median may be between two data values and may not be in the middle of the box plot.

Which is a weakness of the mode? Select one: A. It is usually about the same as the median. B. It does not apply to qualitative data. C. It is hard to calculate when n is small. D. It is inappropriate for continuous data.

D. It is inappropriate for continuous data. -Mode is helpful for categorical data and is easy to calculate in small samples, but requires sorting the sample. Continuous (decimal) data generally have no mode, or, if a mode exists, it is often not near the center.

The mode is least appropriate for: Select one: A. discrete data. B. categorical data. C. Likert scale data. D. continuous data.

D. continuous data. -Mode is good for discrete or categorical data but fails for continuous data.

Which statement is false? Select one: A. The mean from a frequency tabulation may differ from the mean from raw data. B. The skewness coefficient is zero in a sample from any normal distribution. C. The coefficient of variation cannot be used when the mean is zero. D. The standard deviation is in the same units as the mean (e.g., kilograms).

B. The skewness coefficient is zero in a sample from any normal distribution. -Normal populations are symmetric, but a sample may differ from the population.

Regarding probability, which of the following is correct? Select one: A. The probability of the union of two events can exceed one. B. When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events. C. When events A and B are mutually exclusive, then P(A∩B) = P(A) + P(B). D. The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B.

B. When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events.

Which statement is true? Select one: A. If we sample a normal population, the sample skewness coefficient is exactly 0. B. With nominal data we can find the mode. C. Business and economic data are rarely skewed to the right. D. Outliers distort the mean but not the standard deviation.

B. With nominal data we can find the mode. -The mode works well for nominal data.

At Dolon General Hospital, 30 percent of the patients have Medicare insurance (M) while 70 percent do not have Medicare insurance (M´). Twenty percent of the Medicare patients arrive by ambulance, compared with 10 percent of the non-Medicare patients. If a patient arrives by ambulance, what is the probability that the patient has Medicare insurance? Select one: A. .5000 B. .1300 C. .7000 D. .4615

D. .4615 -Review Bayes' Theorem, and perhaps make a table or tree. P(A∩B)/ P(B) 6% of patients have Medicare and arrive by ambulance = (0.2)(0.3) 7% of patients don't have Medicare and arrive by ambulance = (0.1)(0.7) 13% of patients arrive by ambulance, so, 6/13 = 0.4615 = probability that the patient arriving by ambulance has Medicare Insurance

The 25th percentile for waiting time in a doctor's office is 19 minutes. The 75th percentile is 31 minutes. The interquartile range is: Select one: A. impossible to determine without knowing n. B. 22 minutes. C. 16 minutes. D. 12 minutes.

D. 12 minutes. -The IQR is 31 - 19 = 12.

The 25th percentile for waiting time in a doctor's office is 19 minutes. The 75th percentile is 31 minutes. Which is incorrect regarding the fences? Select one: A. A waiting time of 70 minutes would be an outlier. B. The upper outer fence is 67 minutes. C. The upper inner fence is 49 minutes. D. A waiting time of 45 minutes exceeds the upper inner fence.

D. A waiting time of 45 minutes exceeds the upper inner fence. -Apply definitions of fences. For example, the upper inner fence is 31 + 1.5(31 - 19) = 49.