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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