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This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.

1

In an editorial, the *Poughkeepsie Journal* printed this
statement: "The median price – the price exactly in between
the highest and lowest – ..." Does this statement correctly
describe the median? Why or why not?

2

The measure of center that is the value that occurs with the greatest frequency is the _______.

4

Which of the following is always true?

A. Data skewed to the right have a longer left tail than right tail.

B. In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.

C. For skewed data, the mode is farther out in the longer tail than the median.

D. The mean and median should be used to identify the shape of the distribution.

5

Pennies made before 1983 are 97% copper and 3% zinc, whereas pennies made after 1983 are 3% copper and 97% zinc. Listed below are the weights (in grams) of pennies from each of the two time periods.

Find the mean and median for each of the two samples.

Does there appear to be a considerable difference in the means?

The mean weight of the pennies made before 1983 is 3.1133 grams.

The median weight of the pennies made before 1983 is 3.10645 grams.

The mean weight of the pennies made after 1983 is 2.4926 grams.

The median weight of the pennies made after 1983 is 2.49315 grams.

Yes, because the difference in the means is more than 5%.

6

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively.

Find the a. mean, b. median, c. midrange, and d. mode for the data.

e. Which car appears to be the safest?

f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

7

Because the mean is very sensitive to extreme values, it is not a resistant measure of center. The trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and the top 10% of the values, then calculate the mean of the remaining values.

For the following credit-rating scores, find (a) the mean, (b) the 10% trimmed mean, and (c) the 20% trimmed mean.

How do the results compare?

8

9

An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1 equals smooth dash yellow, 2 equals smooth dash green, 3 equals wrinkled dash yellow, and 4 equals wrinkled dash green.

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data.

(e) Do the results make sense?

10

11

Below are the range and standard deviation for a set of data.

Use the range rule of thumb and compare it to the standard deviation listed below.

Does the range rule of thumb produce an acceptable approximation? Suppose a researcher deems the approximation as acceptable if it has an error less than 15%.

12

Cans of regular soda have volumes with a mean of 12.01 oz and a standard deviation of 0.11 oz.

Is it unusual for a can to contain 12.11 oz of soda?

13

Cans of regular soda have volumes with a mean of 12.24 oz and a standard deviation of 0.11 oz.

Is it unusual for a can to contain 12.58 oz of soda?

14

Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance.

15

The trend of thinner beauty pageant winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for beauty pageant winners from two different time periods.

Find the coefficient of variation for each of the two sets of data.

Is there a difference in variation between the two data sets?

16

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below.

Find the coefficient of variation for each of the two sets of data.

Is there a difference in variation between the two data sets?

17

Which of the following is NOT a property of the standard deviation?

A. When comparing variation in samples with very different means, it is good practice to compare the two sample standard deviations.

B. The value of the standard deviation is never negative.

C. The standard deviation is a measure of variation of all data values from the mean.

D. The units of the standard deviation are the same as the units of the original data.

19

Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release.

Find the range, variance, and standard deviation of the data set.

If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation?

20

21

Heights of men on a baseball team have a bell-shaped distribution with a mean of 182 cm and a standard deviation of 7 cm.

Using the empirical rule, what is the approximate percentage of the men between the following values?

**a.** 168 cm and 196 cm

**b.** 161 cm and 203 cm

22

23

24

IQ scores are measured with a test designed so that the mean is 103 and the standard deviation is 13. Consider the group of IQ scores that are unusual.

What are the z scores that separate the unusual IQ scores from those that are usual?

What are the IQ scores that separate the unusual IQ scores from those that are usual?(Consider a value to be unusual if its z score is less than –2 or greater than 2.)

25

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: –2.00, –1.00, 0, 1.00, 2.00? Why?

26

28

Which is relatively better: a score of 76 on a psychology test or a score of 45 on an economics test? Scores on the psychology test have a mean of 89 and a standard deviation of 5. Scores on the economics test have a mean of 55 and a standard deviation of 7.

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