91Ó°ÊÓ

To repeat the test in Exercise $10.83$, but use Lap $5$this data.

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

(e) For the mean difference, the paired test static as follows:

Then ENTER all values the OUTPUT will look like this:

Hence, the test statistics is $-3.3065$.

(f) The $p$-value from the output is $0.00138$.
(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.