EBook Problems EDA Var

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EBook Problems Set - Measures of Variation

Problem 1

The standard error of the mean is a name for the standard deviation of the:

  • Choose one answer.
(a) parent population
(b) sample
(c) raw scores
(d) sampling distribution of the mean
(e) sampling distribution of the variance

Problem 2

There is a compay in which a very small minority of males (3%) receive three times the median salary of males, and a very small minority of females (3%) receive one-third of the median salary of females. What do you expect the side-by-side boxplot of male and female salaries to look like?

  • Choose one answer.
(a) Both boxplots will be skewed and the median line will not be in the middle of any of the boxes.
(b) Both boxplots will be skewed, in the case of the females the median line will be close to the top of the box and in the case of the males the median line will be closer to the bottom of the box.
(c) Need to have the actual data to compare the shape of the boxplots.
(d) Both boxplots will be skewed, in the case of males the median line will be close to the top of the box and for the females the median line will be closer to the bottom of the box.

Problem 3

If the observations larger than 40 are deleted, what will happen to the value of the standard deviation?

  • Choose one answer.
(a) It will become larger
(b) It will become smaller
(c) Need more information to answer this question
(d) It will not change

Problem 4

Does the size of the standard deviation of a data set depend on where the center is?

  • Choose one answer.
(a) Yes, the higher the mean, the higher the standard deviation
(b) Yes, because you have to know the mean to calculate the standard deviation
(c) No, the value of the standard deviation is not affected by the value of the mean
(d) No, because the standard deviation is only measuring how the values differ from each other

Problem 5

A 30 item math test was graded using the following procedure: a correct response was scored as +1, a blank response was scored 0, and an incorrect response was scored -1. The maximum possible test score was 30; the lowest score possible was -30. The standard deviation of the test scores for the class was reported to be -2.13. Therefore

  • Choose one answer.
(a) Most students received positive scores
(b) A calculation error was made in determining the standard deviation
(c) Some students received negatives scores
(d) The class performed poorly on this test
(e) The test was too hard for this class

Problem 6

A health study follows a large random sample of children from the time they are born until they are 20 years old. Each year, a variety of measurements are taken. For example, their weight is measured at birth and every year thereafter.

Which sample of measurements will have the largest standard deviation: weight at birth or weight at 16 years old?

  • Choose one answer.
(a) Both should have about the same standard deviation since both samples include the same people.
(b) Weight at 16 years old because there is less variation among infants.
(c) We cannot tell without knowing the means of both samples.
(d) Weight at birth because weights of infants vary considerably from baby to baby.

Problem 7

Suppose that in a certain country, the average yearly income for 75% of the population is below average, what would you use as the measure of center and spread?

  • Choose one answer.
(a) Mean and standard deviation
(b) Mean and interquartile range
(c) Median and interquartile range
(d) Median and standard deviation

Problem 8

Avoiding an accident while driving can depend on reaction time. That time, measured from the moment a driver first sees the danger until he or she gets his or her foot on the brake pedal, is thought to follow the Normal Model with mean = 1.50 seconds and standard deviation = 0.18 seconds. Determine the closest value for the interquartile range for reaction times.

  • Choose one answer.
(a) 1.62 seconds
(b) 1.38 seconds
(c) We cannot determine the statistics unless we have the actual data
(d) 0.24 seconds
(e) 0.67 seconds

Problem 9

The standard error is the standard deviation for which values?

  • Choose one answer.
(a) Sampling distribution of the variance
(b) Distribution of sample proportions
(c) Raw counts
(d) Sample
(e) Parent population

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