A quality inspector wants to compare the average thickness of three different brands of plastic sheets. The inspector takes random samples from each brand and records the thickness (in units of millimeters). The data will be analyzed using a one-way ANOVA test at a $5\%$ level of significance. Which of the following correctly states the null and alternative hypotheses for this scenario?

Which of the following is NOT a required assumption for conducting a one-way ANOVA test?

Suppose you are conducting a two-way ANOVA with factors $E$ ($3$ levels) and $F$ ($2$ levels). Which of the following is NOT a correct null hypothesis for this test?

A civil engineer is comparing the compressive strength of concrete cubes cured using $4$ different methods. A total of $24$ concrete cubes were tested ($6$ cubes per method).

The analysis of variance (ANOVA) calculation has yielded the following Sum of Squares (SS) values:

Sum of Squares Between Groups $\left(S{S}_B\right):600$

Sum of Squares Within Groups $\left(S{S}_W\right):400$

Based on this data, what is the value of the $F$-test statistic?

A university researcher wants to determine whether the average number of study hours per week differs based on students' primary study environment. Students report their weekly study hours while studying in one of four primary environments: Library, Home, Coffee Shop, or Campus Lounge.

The researcher performs a one-way ANOVA using the collected data and obtains the following results:

Mean Square Between Groups (MSB): $16.0992$

Mean Square Within Groups (MSW): $0.4193$

Degrees of Freedom Between Groups: $3$

Degrees of Freedom Within Groups: $16$

At the $\alpha =0.05$ level of significance, can you conclude that the mean number of study hours differs by primary study environment?