In the one-way ANOVA example comparing calorie estimates among three groups, why does the researcher reject the null hypothesis?

A researcher is conducting a one-way ANOVA to compare calorie estimates among three groups (psychology majors, nutrition majors, and dieticians). Arrange the steps below in the correct logical sequence for performing the statistical test and reaching a conclusion based on the research process.

In the calorie estimate study example, if the between-groups mean square (MSB) were changed to 1,800.00 while the within-groups mean square (MSW) remained 602.23, the researcher would fail to reject the null hypothesis because the resulting F ratio would be less than the critical value of 3.467.

A health psychologist conducts a one-way ANOVA to compare calorie estimates between psychology majors, nutrition majors, and dieticians. Match each numerical value from the study's results to the specific statistical role it plays in analyzing the group differences.

Imagine you are a researcher tasked with designing a new study that replicates the statistical structure of the one-way ANOVA example involving calorie estimates. Which of the following research plans correctly constructs a design that involves three distinct groups and a single numerical measurement?

In the health psychologist's one-way ANOVA example comparing calorie estimates, arrange the following groups in order from the lowest reported sample mean estimate to the highest reported sample mean estimate.

In the health psychology example, an $F$ ratio of 9.92 indicates that the variability between the group means (psychology majors, nutrition majors, and dieticians) is approximately ten times larger than the variability found within the groups.

In a health psychology study comparing calorie estimates among psychology majors, nutrition majors, and dieticians, a researcher calculates an $F$ ratio of 9.92 and finds the critical value to be 3.467. To evaluate the null hypothesis ($H_0: \mu_1 = \mu_2 = \mu_3$) at an alpha level of .05, the researcher determines that because the calculated statistic exceeds the critical value, the most appropriate statistical decision is to _____ the null hypothesis.

Match each ANOVA component from the calorie-estimate study to the specific aspect of variability it measures in the analysis.

After obtaining $F(2, 21) = 9.92$, $p = .0009$, a health psychologist concludes: 'These results prove that professional dietary training causes more accurate calorie estimation.' A peer reviewer should judge this causal conclusion as _____, because the one-way ANOVA compared pre-existing groups without random assignment, making it impossible to rule out alternative explanations for the observed group differences.

Identify the three groups compared by the health psychologist in the provided one-way ANOVA example, recall their respective sample mean calorie estimates, and state the final statistical conclusion of the analysis.

Based on this context, justify the researcher's decision to reject the null hypothesis and explain the meaning of this statistical decision in relation to the population mean calorie estimates of the three groups.

Imagine a researcher replicates this study with new samples of the same size and finds a between-groups mean square ($MS_B$) of 6,022.30 and a within-groups mean square ($MS_W$) of 602.23. Using the critical value of 3.467, calculate the new $F$ ratio and state whether the researcher should reject the null hypothesis.