Semester 1 Final Exam Review

For a sample of 42 rabbits, the mean weight is 5 pounds and the standard deviation of weights is 3 pounds.  Which of the following is most likely true about the weights for the rabbits in this sample?

• The distribution of weights is approximately normal because the sample size is 42, and therefore the central limit theorem applies.

• The distribution of weights is approximately normal because the standard deviation is less than the mean.

• The distribution of weights is skewed to the right because the least possible weight is within 2 standard deviations of the mean

• The distribution of weights is skewed to the left because the least possible weight is within 2 standard deviations of the mean.

• The distribution of weights has a median that is greater than the mean.

Which of the following is a key distinction between well designed experiments and observational studies?

• More subjects are available for experiments than for observational studies.

• Ethical constraints prevent large-scale observational studies.

• Experiments are less costly to conduct than observational studies

• An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot.

• Tests of significance cannot be used on data collected from an observational study.

The correlation between two scores X and Y equals 0.8. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and Y would be 

• -0.8

• -0.2

• 0

• 0.2

• 0.8

Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week.  You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel once a week.  Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber’s behavior in this simulation?

• Assign “0, 1, 2” as watching the shopping channel at least once per week and “3, 4, 5, 6, 7, 8, 9” as not watching.

• Assign “0, 1, 2, 3” as watching the shopping channel at least once per week and “4, 5, 6, 7, 8, 9” as not watching.

• Assign “1, 2, 3, 4, 5” as watching the shopping channel at least once per week and “6, 7, 8, 9, 0” as not watching.

• Assign “0” as watching the shopping channel at least once per week and “1, 2, 3, 4, 5” as not watching; ignore digits “6, 7, 8, 9”.

• Assign “3” as watching the shopping channel at least once per week and “0, 1, 2, 4, 5, 6, 7, 8, 9” as not watching.

Lauren is enrolled in a very large college calculus class.  On the first exam, the class mean was 75 and the standard deviation was 10.  On the second exam, the class mean was 70 and the standard deviation was 15.  Lauren scored 85 on both exams.  Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class?

• She scored much better on the first exam.

• She scored much better on the second exam

• She scored about equally well on both exams

• It is impossible to tell because the class size is not given

• It is impossible to tell because the correlation between the two sets of exam scores is not given.

The boxplots shown summarize two data sets, I and II.  Based on the boxplots, which of the following statements about these two data sets CANNOT be justified?

• The range of data set I is equal to the range of data set II

• The interquartile range of data set I is equal to the interquartile range of data set II

• The median of data set I is less than the median of data set II

• Data set I and data set II have the same number of data points.

• About 75% of the values in data set II are greater than or equal to about 50% of the values in data set I.

A complex electronic device contains three components, A, B, and C.  The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04 respectively.  If any one component fails, the device will fail.  If the components fail independently of one another, what is the probability that the device will NOT fail in one year?

• Less than 0.01

• 0.078

• 0.080

• 0.922

• Greater than 0.99

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes.  If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

• 0.16

• 0.32

• 0.50

• 0.84

• 1.00

A least squares regression line was fitted to the weight (in pounds) versus age (in months) of a group of many young children.  The equation of the line is

y-hat=16.6+0.65t  , where y-hat is the predicted weight and t is the age of the child.  A 20-month old child in this group has an actual weight of 25 pounds.  Which of the following is the residual weight in pounds for this child?

• -7.85

• -4.6

• 4.6

• 5

• 7.85

A police officer is using a radar device to check motorists’ speeds.  Prior to beginning the speed check, the officer estimates that 40% of motorists will be driving more than 5 mph over the speed limit.  Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 mph over the speed limit?

• 0.0256

• 0.1296

• 0.3456

• 0.8704

• 0.9744