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?

Determine the critical $F$-value for a right-tailed test at $\alpha =0.10$ with numerator degrees of freedom $d.f.N=7$ and denominator degrees of freedom $d.f.D=12$.

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

What is the critical $F$-value for a two-tailed test with $\alpha =0.20$, numerator degrees of freedom $d.f.N=8$, and denominator degrees of freedom $d.f.D=16$?

A tech recruiter is analyzing the starting salaries (in units of USD) of entry-level software engineers in six major U.S. cities to determine whether location influences pay. Salaries were collected from a random sample of five job offers in each of the following cities: San Francisco, Austin, New York, Denver, Chicago, and Atlanta. The mean square between groups (MSB) is $105,023,283.34$, and the mean square within groups (MSW) is $2,976,333.33$. At $\alpha =0.05$, can you conclude that the mean starting salary differs for at least one of the cities?

Determine the critical $F$-value for a right-tailed test if $\alpha =0.01$, numerator degrees of freedom $d.f.N=4$, and denominator degrees of freedom $d.f.D=6$.

A university administrator claims that the variance in student satisfaction scores for online courses is less than the variance for in-person courses. A random sample of $22$ online course students has a satisfaction score variance of $1.5$. A random sample of $16$ in-person course students has a variance of $3.2$. At $\alpha =0.01$, is there enough evidence to support the administrator's claim?

A quality inspector wants to compare the average thickness of three different brands of plastic sheets. She 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?

Researchers examined whether daily paternal alcohol consumption during the partner's pregnancy is associated with neonatal birth length. They reported that their results were "adjusted for potential confounders." What is the most accurate interpretation of this phrase in the context of their analysis?

A pharmaceutical company claims that the variability in the effectiveness of its new drug is less than that of a competitor's drug. A sample of $15$ patients using the new drug has a variance of $1.2$, while a sample of $20$ patients using the competitor's drug has a variance of $2.8$. At $\alpha =0.01$, is there enough evidence to support the company's claim?