A paired difference experiment compared two methods (x1 and x2) and found a mean difference (d) of 3.5 with a standard deviation (sd) of 3.5. To test the null hypothesis that the true difference is 0 against the alternative that x1 is less than x2, the z-statistic must be less than -1.282 for a one-tailed test with α=0.1. Since the calculated z-statistic is not in the rejection region, there is not enough evidence to reject the null hypothesis.

1. A paired difference experiment produced the following results: [40 Points] nd=38x1=92x2=95.5xd=
3.5sd2=21 a. Determine the values of z for which the null hypothesis, 12=0, would be rejected in
favour of the alternative hypothesis, 12<0. Use =0.10. [20 Points] Lower-tailed, level of
significance ()=0.1, Rejection region z<1.282[You may verify this with
z_statistic_rejection_region.py] b. Conduct the paired difference test described in part a. Draw the
appropriate conclusions. [20 Points]