Exam #2

As part of pharmaceutical testing for sleepiness as a side effect of a drug, 200 patients are randomly assigned to one of two groups of 100 each. One group is given the actual drug and the other a placebo. The number of people who felt sleepy in the next hour is recorded as Drug Placebo Sleepy 40 20 Not Sleepy 60 80 28a. What is the probability that a randomly picked patient in the study feels sleepy in the next hour? 28b. what is the probability that a randomly picked patient in the study takes the placebo of feels sleepy in the next hour? 28c. Given that the patient was given the drug, what is the probability that he or she feels sleepy in the next hour? 28d. is whether a patient feels sleepy independent of taking the drug? Explain using probabilities.

28a. 0.30 28b. 0.70 28c. 0.40 28d. Not independent Explanation: The contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. The conditional probability is calculated as P(B|A) = P(A n B) /P(A) Two events, A and B, are independent if and only if P(A|B) = P(A), or P(B|A) = P(B). a. P(Drowsy) = (40 + 60)/200 = 0.30 b. P(Placebo OR Drowsy) = (40 + 20 + 80)/200 = 0.70 c. P(Drowsy|Drug) = 40/(40 + 60) = 0.40 d. Not independent because P(Drowsy) P(DrowsyDrug)

What is the interquartile range?

A. Q3 - Q1 Explanation: The interquartile range (IQR) is the difference between the third and the first quartiles.

The 150 residents of the town Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Chocolate Valilla Swirl Under 25 years old: 40, 20, 15 At least 25 years old 15, 40, 20 What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old?

A: 0.20 Explanation: A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. P(Chocolate / At least 25) = 15 / (15 + 40 + 20) = 0.20

The following graph visualizes frequencies of different combinations of events related to gender, survival status, and passenger class for Titanic passengers. Based on this graph determine visually what is the approximate probability of survival for male passenger in the 1st class.

A: 0.33

Suppose you have a data set with he minimum value 5 and maximum value 25. Moreover, you calculated in R that the first quartile, Q1, is 10, while third quartile,Q3, is 15. What can you conclude whether % and 25 are outliers?

A: 5 is not an outlier, 25 is an outlier

Which five values are graphed on a box plot?

A: Min, Quartile 1, Quartile 3, Max Explanation: The values are: Minimum, Quartile 1, Median, Quartile 3, and Maximum

A survey of adults who typically work full time from home recorded their current education level. The results are shown in the table below. Education level Frequency Bachelor's degree or higher 32 Associate degree 12 High school only 4 less than high school 2 Calculating the probability that a randomly selected adult who works full time from home has an associate degree is using ___________ probability.

A: empirical Explanation: Relative frequencies are used to calculate the empirical probability of event

Suppose you created the following contingency table and name ct2 in R. Now you would like R to create a table showing conditional probabilities of survival given the person is a male/female. Which of the following commands should you execute?

A: prop.table(ct2, margin=2)

Suppose you are analyzing Titanic passengers data set in R stored in a data frame t and you want to create a contingency table with two variables: one measuring whether Titanic passenger survived or not, another identifying the gender of a passenger. Which of the following commands should you execute?

A: table(t$survived, t$sex)

Suppose you want to generate an artificial dates with 10000 observations in R from a normal population with mean = 100 and standard deviation = 20. Which of the following commands should you execute?

A: x <- rnorm(n=10000, mean=100, sd=20)

The average class size this semester in the business school of a particular university is 38.1 students with a standard deviation of 12.9 students. The z-score for a class with 21 students is ________.

A:-1.33 Explanation: The z-score is computed as ( x - x' )/ s

A business statistics class roster includes 14 business major students and 21 students of another major. Sixteen students in this class are male. There are eight female business majors. What is the number of men in the class who are not business majors?

B. 10 Explanation: The contingency table shows frequencies for two qualitative or categorical variable, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values.

For an experiment in which a single die is rolled, the sample space may be {1,2,3,4,5}.

B.false Explanation:

The 150 residents of the town Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Chocolate Valilla Swirl Under 25 years old: 40, 20, 15 At least 25 years old 15, 40, 20 What is the probability that a randomly selected customer prefers vanilla?

B: 0.40 Explanation: A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. P(Vanilla) = ( 20 + 40 ) / 150 = 0.40

Which of the following statements is most accurate when defining percentiles?

B: Approximately (100 - p)% of the observations are greater than the 4th percentile. Explanation: Approximately p% of the observations are less than the pth percentile, and approximately (100-p)% of the observations are greater than the 4th percentile.

Subjective probability is assigned to an event by drawing on logical analysis

B: False

The complement of an event A, denoted by Ac, within the sample space S, is the event consisting of all outcomes of A that are not in S.

B: False

A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n)___________.

B: classical probability Explanation: Empirical probability refers to probability inferred through relative frequencies, whereas subjective probability refers to probability based on personal experience and judgement.

The graph below shows positions of cutoff values that divide the dates on equally sized (in terms of observations) classes. What is the name of the cutoffs?

B: deciles

This graph is not part of the base R packages, so you need to download an external package. Which package is needed?

B: lattice

Suppose you created the following contingency table and named it ct2 in R. Now you would like R to create a table showing conditional probabilities of survival given the person is a male/female. Which of the following commands should you execute?

B: prop.table(ct2)

Which of the following capabilities does Analysis of Relative Location provide?

B: they make statements regarding the percentage of data values that fall within some number of standard deviation from the mean. Explanation: Both Chebyshev's Theorem and the Empirical Rule provide estimates the proportion of the data that lie within a specified number of standard deviations front the mean.

Which of the following is true when using the empirical rule for a set of sample data?

B:approximately 68% of all observations are in the interval x' ± s Explanation:For a set of sample data, the empirical rule states that approximately 68% of all observations are in the interval x ± s, approximately 95% of all observations are in the interval x ± 2s, and almost all observations are in the interval x ± 3s.

The 150 residents of the town Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Chocolate Valilla Swirl Under 25 years old: 40, 20, 15 At least 25 years old 15, 40, 20 What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?

C: 0.60 Explanation: A contingency table shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values. A more convenient way of calculating relevant probabilities is to convert the contingency table to a joint probability table. P(Swirl U At least 25) = ( 15+40=20+15)/ 150 = 0.60

Which of the following represents a subjective probability?

C: A skier believes she has a 10% chance of winning a gold medal. Explanation: For well-defined problems an a priori probability can be calculated by resining about the problem. A subjective probability is based on personal experience and judgment.

Suppose you want to compare how the distribution of chicken weights depends on the type of food chickens eat. You would create this graph. which of the following commands should you execute?

C: boxplot(chickwts$weight ~ chickwts$feed)

The intersection of events A and B denoted by A n B, _______________.

C: contains outcomes that are both in A and B Explanation: The intersection of two events, A n B, is the event consisting of all outcomes in both A and B.

In an accounting class of 200 students, the mean and standard deviation of scores was 70 and 5, respectively. Use the empirical rule to determine the number of students who scored less than 65 or more than 75.

C: it is about 32 Explanation: Between 65 and 75 is one standard deviation which is about 68 percent. Then, the percentage less than 65 or more than 75 would be 100 68 = 32 percent.

You built this box chart in R. The last box chart has dots. What does the dot mean?

C: maximum value of the variable which IS an outlier

suppose you want to find 10% percentile for your variable x in R. Which of the following commands should you execute?

C: quantile (x, 10/100)

The intersection of events A = [apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________.

C: {pumpkin pie} Explanation: The intersection of two events, A n B, is the event consisting of all outcomes in both A and B.

A sample space contains ___________.

D: all possible outcomes of an experiment Explanation: The sample space must consist of all possible outcomes of an experiment

Suppose you want to build a box chart for a variable X in R. Which of the following commands should you execute?

D: box plot (x)

When using the empirical rule, which fo the following assumptions is made?

D: the data are approximately symmetric and bell-shaped Explanation: For both sample and population data, the empirical rule is applicable when the data are approximately symmetric and bell-shaped. The data does not have to be exactly symmetric and bell-shaped as very few, if any, datasets in the real world are perfect.

For the sample space S = [apple pie, cherry pie, peach pie, pumpkin pie}, what is the complement of A = {pumpkin pie, cherry pie}?

D:{apple pie, peach pie} Explanation: The complement of event A, Ac, is the even consisting of all outcomes in the sample space S that are not in A

Mark's grade on the recent business statistics test was an 85 on a scale of 0-100. Based on this information we can conclude that Mark's grade was in the 85th percentile in his class. A. True B. False

False

The formula for z-score is = x'-x/s A. True B. False

False

The median is not always the 50th percentile A. True B. False

False

In a data set, an outlier is a large or small value regarded as an extreme value in the data set A. True B. False

True

the empirical rule is only applicable for approximately bell-shipped data A. True B. False

True