91Ó°ÊÓ

To conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices by using the data from Lap 1 only.

(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 practice is denoted by $\stackrel{¯}{X_1}-\stackrel{¯}{X_2}$.
(d) Student's t distribution is $t_{20.32}$.
(e) For the mean difference, the paired test static as follows:

After ENTER all of the values, the OUTPUT will look like this:

Hence, the test statistic as: $-4.70$.

(f) The $p$-value from the output is $0.0001$

(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 sufficient evidence to conclude that the mean time for completing a lap in races is different from that in practices at the $5\%$significance level.