Statistics

13.11

Top Ten Business Computability PC Connection

Software Packages Price ($) Price ($)

Windows 95 Upgrade 88 95

Norton Anti-Virus 59 70

McAfee ViruScan 49 60

First Aid 97 Deluxe 54 58

Clean Sweep III 37 37

Norton Utilities 68 75

Netscape Navigator 45 40

MS Office Pro 97 Upgrade 300 310

First Aid 97 32 35

Win Fax Pro 95 95

(a) Calculate the differences between the prices for each type of
software package. Just looking at the differences, do you think that one
company charges more than the other? Why or why not?

(b) Calculate the average difference and the standard deviation of the
differences.

(c) Set up the hypotheses to test whether the mean difference in price
between the two companies is zero.

(d) Assuming that the data are normally distributed, at the 0.05 level
of significance, is there a difference in the mean price of software for
the two companies?

(e) Did these results differ from the last time you analyzed the data?
Why do you think this happened?

13.31

(a) Look at the data again. Does any software have a price that seems to
be very different from the others? If so, which one?

(b) Drop the data for the unusual observation and perform the hypothesis
test again using the test for independent samples.

(c) Does anything change from the last time you did the test? If so,
what?

(d) Does dropping the observation change the decision?

(e) Do you think this was the right test to use? Why or why not?

13.28 The nurses who were part of the hand-washing experiment are still
not convinced that the length of time spent washing hands makes that
much difference. They design their own study and decide to have each
nurse in the CCU wash his or her hands twice, once

for 2.5 seconds and once for 15 seconds. After each washing they do a
bacteria culture and measure the number of bacteria that remain on the
person's hands. The data are shown in the next table.

Culture 1 Culture 2

Observation 2.5 s 15 s

1 66 78

2 132 115

3 120 93

4 187 48

5 190 77

6 17 3

7 33 12

8 92 12

9 1000 146

(a) Calculate the differences between the number of bacteria for each
nurse. Just looking at the differences, do you think that washing longer
decreased the amount of bacteria? Why or why not?

(b) Calculate the average difference and the standard deviation of the
differences.

(c) Set up the hypotheses to test whether there was a decrease in the
average amount of bacteria after washing longer.

(d) Assuming that the data are normally distributed, at the 0.05 level
of significance, what can you conclude?

(e) Suppose that you were told that the second episode of hand washing
was done right after the first. Would that change the way you interpret
the results of the study?