For a right-tailed ANOVA test, what is the critical $F$-value when $\alpha =0.10$, numerator degrees of freedom $8$, and denominator degrees of freedom $18$?

At the $\alpha =0.025$ significance level, test the claim that ${\sigma }_1^2\le {\sigma }_2^2$ for two normal populations. Sample data: $s_1^2=950,n_1=9$; $s_2^2=890,n_2=8$. What is the correct conclusion?

A company claims that the variability in production time at Plant X is greater than at Plant Y. At $\alpha =0.10$, the sample statistics are: $s_1^2=950,n_1=10$ and $s_2^2=800,n_2=12$. Test the claim ${\sigma }_1^2>{\sigma }_2^2$.

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 $d.f.D=12$.

Determine the critical $F$-values for a two-tailed test with $\alpha =0.10;d.f.N=10$ and $d.f.D=30$.

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?

You are comparing the variability of two different teaching methods using a two-sample $F$-test. If the first group has $22$ students and the second group has $17$ students, what are the appropriate degrees of freedom for the numerator and denominator?

Determine the right and left-tailed critical $F$-values for a two-tailed test with $\alpha =0.02$, $d.f.N=8$, and $d.f.D=25$.

A researcher claims that the variance of population 1 is greater than that of population 2. At the $\alpha =0.05$ significance level, test this claim using the following sample statistics: $s_1^2=61.5,n_1=20$ and $s_2^2=55.0,n_2=15$. Assume both populations are normal and samples are independent.

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?

A researcher wants to test whether the variance of test scores in School A is greater than that in School B at the $\alpha =0.05$ significance level. The sample variances and sizes are: $s_1^2=520,n_1=7$ for School A and $s_2^2=410,n_2=8$ for School B. Assume both populations are normally distributed and samples are independent. What is the correct decision regarding the claim ${\sigma }_1^2>{\sigma }_2^2$?

Determine the critical $F$-value for a right-tailed test where $\alpha =0.01$, numerator degrees of freedom $d.f.N=3$, and denominator degrees of freedom $d.f.D=15$.

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 $d.f.D=6$.

What is the critical $F$-value for a right-tailed test with $\alpha =0.025$, numerator degrees of freedom $d.f.N=12$, and denominator degrees of freedom $d.f.D=18$?

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