91Ó°ÊÓ

To repeat the test in Exercise 10.83, but this time combine the data from Laps 1 and 5.

(a) The null hypothesis is defined as follows:
$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2$
(b) The alternate hypothesis is defined as follows:
$H_a:{\mathrm{μ}}_1≠{\mathrm{μ}}_2$
(c) The difference between the mean times for completing a lap in races and in practices is denotes by $\stackrel{¯}{X_1}-\stackrel{¯}{X_2}$
(d) Student's t distribution.
(e) The paired test static for the mean difference is,

After ENTER all values the OUTPUT will look like this:

Hence, the test statistics $-5.087$.

(f) The $p$-value from the output is $0.0000084$.
(g) Using the data from the last exercise, create a mental picture of the situation.
The horizontal axis should be clearly labelled and scaled, and the $p$-value-corresponding region(s) on the graph should be shaded.

(h)

(i) $\mathrm{Î\pm }=0.05$
(ii) Decision: Null hypothesis is rejected.
(iii) $\mathrm{Î\pm }>p$-value
(iv) Conclusion: There is enough evidence to conclude that the mean time for completing a lap in races is different from that in practices, at the $5\%$significance level.