Practice Questions

 1.         (4 points) Researchers from a psychiatry department are examining the effectiveness of a new medication on moderate-to-severe symptoms of anxiety. The study requires volunteers who are at least 18 years old and in general good health and who are not taking oral medications for their anxiety. The study lasts 23 weeks. The researchers are offering a small payment as a compensation for participation.

Is this an ideal data collection method? Can the results be considered reliable? Can the gathered data be representative of the population?

Give two reasons to support or reject the method of recruiting volunteers to gather information in this statistical study.

2.   (10 points) 24 students were randomly selected and asked how many CDs they owned. Their answers were as follows:

55  30  60  5  50  20  35  67  75  0  30  59  25  68  15  20  70  35   65  25  30  48  50  45..Find the mean, median, and mode, which best describes the number of CDs owned.

(b.)             Draw a box plot for this data, clearly labeling the minimum, maximum, and first and third quartiles. (Note: if you are not able to draw a boxplot, list the points that would be a part of that plot.)

(c.)              What is the standard deviation? What does this tell you about the data?

 3.         (6 points) X is a variable of random numbers between 0 and 5; X has a uniform distribution

(a.)       On another page, draw a picture of the distribution (you will not need to turn this in).  What does it look like? 

(b.)       Find P(X<2)  

(c.)       Find P(1<X<3)

4.         (6 points) A computer software supplier has developed a new record-keeping package for use by hospitals. The company feels that the probability that the new package will show a profit in its first year is 0.6, unless a competitor introduces a product of comparable quality this year, in which case the probability of a first-year profit drops to 0.3. The supplier suggests that there is a 50-50 chance (there is a 50% probability) that a comparable product will be introduced this year. Define the following events:

A.A competitor introduces a comparable product.  

B.The record-keeping package is profitable in its first year.

(a.)       What is the probability that both A and B will occur?

(b.)       What is the probability that either A or B will occur?

5.         (5 points) The following table gives the distribution of hours of study for a class.

(a.)       What is the average number of hours studied for this class?

(b.)       What is the standard deviation?

6.         (4 points) A standard deviation is

            (a.) A measure of central tendency

            (b.) Useful in doing scatterplots

            (c.) A measure of variation in data

            (d.) Is always between -1 and +1

7.         (10 points) Christine went for a routine medical exam. The next morning, her physician phoned to tell her that one of her tests came back positive, indicating she may have disease D. The physician told her that the probability that the test will be accurate is 0.95. According to the physician, even though only 1% of women of Christine’s age actually has D, the test is a good indicator that Christine may have the disease. When someone does not have D, the probability that the test is correctly negative is 0.95.

(a.)              Draw a tree diagram for all possible outcomes.

(b.)             What is the probability that Christine’s test is positive?

9.         (6 points) Suppose that vehicle speeds (X) at a highway location have a normal distribution with a mean of 62 mph and standard deviation of 5 mph.

(a.)       What is the probability that the speed of a randomly selected vehicle at this location is between 60 and 70 mph?

(b.)       What is the probability that the speed of a randomly selected vehicle at this location is less than 55 mph [P(X<55)]?

10.       (10 points) The following table includes data about the height, in inches, of adult males and the height of their parents.

(a.)       Use your calculator to do scatterplots for these data.  Which is the independent variable?  Which is the dependent variable?  Describe what the plot looks like. Are there any outliers?

(b.)       From your plot(s), can you tell if there is a relationship between the heights of sons and their parents? 

Is the relationship between the son and his mother or father greater than the other?  How can you tell? 

What are the correlations?

(c.)       Write a linear equation for the relationship between the heights of sons and their fathers.

(d.)      Using that equation, how tall would you expect the son of a 6.4 feet (76.8 inches) father to be?

11.       (1 point each/9 points total) Fill in the blank spaces.

To identify a particular normal curve, you must know the __________ and __________ for that distribution. To convert a particular normal curve to the standard normal curve, you must convert original observations into __________. Although there are an infinite number of different normal curves, there is __________ standard normal curve. The standard normal curve has a __________ of zero and a __________ of one. A z score indicates how many __________ an observation is __________ or __________ the mean of the distribution.

12.       (10 points) The following data represent the number of driver fatalities (in thousands) in the United States in 2002 by age for male and female drivers.

(a.)       What is the probability that a randomly selected fatality is a male between 16 and 20?

(b.)       What is the probability that a fatality is a female?

(c.)       If we know that the driver was a female, what is the probability that she was 70 or over?

(d.)      What is the probability that a driver fatality was either a female or between 35 and 54?

(e.)       If a driver fatality was between the ages of 16 and 20, was it more likely to be a male or a female?