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

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

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

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

The null and alternative hypothesis is given by,

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

We have, ${\mathrm{H}}_{\mathrm{a}}:{\mathrm{\mu }}_1\ne {\mathrm{\mu }}_2$

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

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

Let ${\overline{\mathrm{x}}}_2$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