Microsoft Office Tutorials and References
In Depth Information
Fortunately, we have an important tool available in our Descriptive Statistics
that helps us with sampling results— Confidence Level . We can choose a particu-
lar level of confidence , 95% in our case, and create an interval about the sample
mean, above and below. If we sample 100 teens many times from our potential teen
population, these new confidence intervals will capture the true mean of new web-
page visits 95% of the times we sample. In Exhibit 3.29 we can see the Confidence
Interval for 95% at the bottom of the descriptive statistics. Make sure to check the
Confidence Level for Mean box in the Descriptive Statistics dialogue box to return
this value. A confidence level of 95% is very common and suitable for our appli-
cation. So our 95% confidence interval for the mean of the new website is 11.83
±
0.74832
, or approximately the range 11.08168 to 12.57832. For the old website,
the confidence interval for the mean is 7.54
...
, or the range 6.94814 to
8.13186. Note that the low end of the mean for the new website views (11.08168)
is larger than the high end of the mean for the old views (8.13186). This strongly
suggests with statistical confidence, that there is indeed a difference in the page
views.
Next, we can expand on the analysis by not only considering the two categories,
positive and non-positive differences, but also the magnitude of the differences. This
is an opportunity to use the Histogram tool in Data Analysis . We will use bins
values from –6 to 16 in one unit intervals. These are the minimum and maximum
observed values, respectively. Exhibit 3.31 shows the graphed histogram results of
the column E ( Delta ). The histogram appears to have a central tendency around the
range 2 to 6 web-pages, which leads to the calculated mean of 4.29. It also has a very
minor positive skew. For perfectly symmetrical distributions, the mean, the median,
and the mode of the distribution are the same and there is no positive or negative
skew. Finally, if we are relatively confident about our sample of 100 teens being
representative of all potential teens, we are ready to make a number of important
statements about our data, given our current analysis:
±
0.59186
...
1. If our sample of 100 teens is representative, we can expect an average improve-
ment of about 4.29 pages after the change of the new web-site design.
2. There is considerable variation in the difference between new and old (Delta)
evidenced by the range,
6 to 16. There is a central tendency in the graph that
places many of the Delta values between 2 and 6.
3. We can also make statements such as: (1) I believe that approximately 21%
of teens will respond negatively, or not at all, to the web-site changes; (2)
approximately 51% of teens will increase their page views by 2 to 6 pages; (3)
approximately 24% of teens will increase page views by 7 or more pages. These
statements are based on the 100 teen samples we have taken and will likely vary
somewhat if another sample is taken. If these numbers are important to us, then
we may want to take a much larger sample to improve of chances of stability in
these percentages.
4. Our 95% confidence interval in the new website mean can be stated as 11.83
±
0.74832
...
. This is a relatively tight interval. If a larger number of observations
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