Question

It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of $31$females had a mean score of $82$with a standard deviation of three, and a random sample of $25$males had a mean score ofrole="math" localid="1650387947130" $76$ with a standard deviation of four.

Short answer

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

Step-by-step solution

Given information

It is believed that average grade of females is more than the males on an English essay in a specific school system.

31 random females had mean score of $82$and standard deviation of $3.$

25 random males had mean score of $76$and standard deviation of $4.$

Calculation

Now solving,

Assuming average grade of females as${\mu }_F.$

Assuming average grade of makes as${\mu }_M.$

The null and alternative hypothesis is obtained as :-

$$\begin{gathered} {\mathrm{H}}_0:{\mu }_{\mathrm{F}}={\mu }_{\mathrm{M}} \\ {\mathrm{H}}_{\mathrm{a}}:{\mu }_{\mathrm{F}}>{\mu }_{\mathrm{M}} \end{gathered}$$

This shows that this hypothesis testis for independent group means, population standard deviations, and/or variances unknown.

Final answer

This shows that this hypothesis testis for independent group means, population standard deviations, and/or variances unknown.