A data analyst is conducting a study to determine if the mean number of courses taken in a college semester is statistically the same between freshmen, sophomores, juniors, and seniors.

To collect data for this ANOVA test, the statistician randomly selects students attending college and records their year and the number of courses each is taking in the current semester, as shown in the table below. Assume the conditions necessary for a one-way ANOVA are met.

SHOW ALL STEPS OF THE 5 STEP HYPOTHESIS TEST FOR THIS ONE-WAY ANOVA INCLUDING

1) Determining the null and alternate hypothesis

2) Draw a diagram of the critical regions including the critical value and how you got it

3) Calculate the test statistic (rounded to two decimal places) showing all formulas and calculations below the skeleton of the ANOVA Table

4) decide whether to reject or not reject and finally

5) Answer the below question.

At a 5% significance level, do the data provide sufficient evidence to conclude that a difference exists among the four class levels in the mean number of courses taken in a college semester?

FRESHMEN 6,7,4,4,6

SOPHOMORE 6,5,5,5,4

JUNIOR 5,4,5

SENIOR 3,4,4,4,5,8