Question

Use the following information to answer the next $15$exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

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 of $76$ with a standard deviation of four

Short answer

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

Step-by-step solution

Given information

Females are thought to get a higher average grade on an English essay in a certain educational system than males.

The mean score of $31$random females was $82$, with a standard deviation of$3$.

The mean score of $31$random females was$82$, with a standard deviation of $4$.

Explanation

Assuming a female's average grade is ${\mu }_F$

Assuming a male's average grade is ${\mu }_M$

The null and alternative hypothesis is given as

$$\begin{gathered} H_0:{\mu }_F={\mu }_M \\ {H}_a:{\mu }_F>{\mu }_M \end{gathered}$$

This demonstrates that the hypothesis test is valid for independent group means, population standard deviations, and unknown variances.