11.Â Â How would increasing
the standard deviation of the number of close friends for both males and
females (all else remaining the same) change the p-value? Why? As we saw
earlier, another measure of the strength of evidence against the null
hypothesis would be to standardize the statistic by subtracting the
hypothesized value and dividing by the standard error of the statistic.
12.Â Â On the left side of
the applet (below the Sample data window) use the Statistic pull-down menu to
select the t-statistic (again, there will be a pause). Record the value of the
t-statistic that is computed for your data. Write a one-sentence interpretation
of this value. Notice that the standardized statistic uses the letter t (the
one you should remember from Chapter 3) instead of the z (from Chapters 1 and
5) we saw when testing proportions. This is because the theoretical
distribution used is now a t-distribution instead of a normal distribution.
These t-distributions are very similar to normal distributions especially when
sample sizes are large. The t-statistic, like the z-statistic, tells us how
many standard deviations our sample difference is above or below the mean and
it can be judged in the same manner. More details about the t-statistic are
given earlier in this section and in the Calculation Details appendix.