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# Test of hypothesis for difference between means

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13.11
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Software Packages Price (\$) Price (\$)
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Norton Utilities 68 75
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(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?