91Ó°ÊÓ

The given data sets are from Terri Vogel's log book.

Let${\mathrm{μ}}_1$be the mean time to complete Lap 1 in races

Let ${\mathrm{μ}}_2$be the mean time to complete Lap 1 in practices

The null and alternative hypothesis is given by,

localid="1653303177214" $$\begin{gathered} {\mathrm{H}}_0:{\mathrm{μ}}_1={\mathrm{μ}}_2{\mathrm{H}}_0:{\mathrm{μ}}_1-{\mathrm{μ}}_2=0 \\ {\mathrm{H}}_{\mathrm{a}}:{\mathrm{μ}}_1≠{\mathrm{μ}}_2{\mathrm{H}}_{\mathrm{a}}:{\mathrm{μ}}_1-{\mathrm{μ}}_2≠0 \end{gathered}$$

We have, ${\mathrm{H}}_{\mathrm{a}}:{\mathrm{μ}}_1≠{\mathrm{μ}}_2$

Here, ${\mathrm{μ}}_1$ is not equal to ${\mathrm{μ}}_2$. Therefore, this is a Two – tailed test.

Let ${\stackrel{¯}{\mathrm{x}}}_1$be the sample mean to complete Lap 1 in races

Let ${\stackrel{¯}{\mathrm{x}}}_2$be the sample mean to complete Lap 1 in practices

Number of random samples in races,localid="1653304155165" ${\mathrm{n}}_1=20$

Number of random samples in races, ${\mathrm{n}}_2=15$

localid="1653306341815">x¯1=Sumofrandomsamplesn1=262720=131.35x¯2=Sumofrandomsamplesn2=207815=138.53

Let ${\mathrm{s}}_1$be the sample standard deviations to complete Lap 1 in races

Let ${\mathrm{s}}_2$be the sample standard deviations to complete Lap 1 in practices