Question

The league mean batting average is 0.280 with a known standard deviation of 0.06. The Rattlers and the Vikings belong

to the league. The mean batting average for a sample of eight Rattlers is 0.210, and the mean batting average for a sample

of eight Vikings is 0.260. There are 24 players on the Rattlers and 19 players on the Vikings. Are the batting averages of the

Rattlers and Vikings statistically different?

Short answer

The test is for known variances, population standard deviations, and/or independent group means.

Step-by-step solution

Given information

The League mean batting average is $0.28$, while the standard deviation is $0.06$.

The league's sample 8 Rattlers' men's batting average is $0.210$.

The men's batting average in sample 8 of the league is $0.260$.

Rattlers have a total of 24 players.

Vikings$=19$ number of players

To identify the most appropriate hypothesis test for the supplied data.

Let us assume the mean batting average of Rattlers as ${\mu }_{\mathrm{ℝ}}$

considering mean batting average of Vikings as ${\mu }_V$

The null and alternative hypothesis is given as

${\mathrm{H}}_0:{\mu }_{\mathrm{R}}={\mu }_V$

${\mathrm{H}}_{\mathrm{a}}:{\mu }_{\mathrm{R}}\ne {\mu }_{\mathrm{V}}$

This demonstrates that this hypothesis test can be used with known independent group means, population standard deviations, and/or variances.