A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of $18$ students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. State the null and alternative hypotheses for a one-way ANOVA test.

"Using Technology to Perform a Two-Way ANOVA Test In Exercises 15–18, use technology and the block design to perform a two-way ANOVA test. Use α=0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

[APPLET] Laptop Repairs The manager of a computer repair service wants to determine whether there is a difference in the time it takes four technicians to repair different brands of laptops. The block design shows the times (in minutes) it took for each technician to repair three laptops of each brand.

"In Exercises 17–20, (a) identify the claim and state H₀ and Hₐ, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

A travel consultant claims that the standard deviations of hotel room rates for Sacramento, CA, and San Francisco, CA, are the same. A sample of 36 hotel room rates in Sacramento has a standard deviation of $51 and a sample of 31 hotel room rates in San Francisco has a standard deviation of $37. At α=0.10, can you reject the travel consultant’s claim? (Adapted from Expedia)"

A company wants to determine whether the average monthly sales differ among three different regions: North, South, and West. The company collects monthly sales data (in thousands of dollars) from four randomly selected stores in each region over the same month. Calculate the F-statistic given the Mean Square due to Treatments: MST = $226.6$ (variance between groups) and the Mean Square due to Error: MSE = $7.944$ (variance within groups).

Four different high schools in local towns took random samples of 100 students in three grades, $10^{th} - 12^{th}$ and collected data on the weekly time spent studying to see if students in each of these grades study on average for the same amount of time per week. The four schools ran ANOVA tests on their samples, and the F-Statistics were $2.35$ , $2.57$ , $2.81$ , and $3.93$ . Which F-Statistic is most likely to indicate the average study times across grades are not all the same?

A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of $18$ students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. An ANOVA test is performed and results in a P-value of $1.403 ∙ 10^{- 7}$ . Interpret these results.

A regional sales director wants to determine whether different customer service training programs lead to different levels of employee performance across three branches. Each branch uses one of the following training programs: Program A. Program B, or Program C. After one month, the director measures the performance score (out of 100) for 5 randomly selected employees from each branch. Using $alpha equals 0.05$ , perform a one-way ANOVA to determine whether there is a statistically significant difference in mean performance among the three training programs.

In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=20,d.f.D=25

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=40,d.f.D=60