Question

For each exercise, assume that all variables are normally distributed, that the samples are independent, and that the population variances are equal. Also, for each exercise, perform the following steps: 1. State the hypotheses and identify the claim; 2. Find the critical value; 3. Compute the test value; 4. Make the decision to reject or not reject the null hypothesis; 5. Summarize the result.

Answer 1

Ho : There is no significant difference between the mean grades of three groups.
Ha : There is a significant difference between the mean grades of three groups.

Level of Significance(l.o.s.) : $\alpha$ = 0.05

Decision Criteria : Reject Ho at 5% l.o.s. if F > F crit,
where F crit = F ($\alpha$, k-1, N-k) = F (0.05, 2, 15) = 3.6823

Calculations : In order to obtain the results, we make use of Excel & the steps are as follows :

Step 1 : Enter the data in Excel.
Step 2 : Select "Anova : Single Factor" function from the data analysis tab available under the data tab of Excel.
Step 3 : Enter the range of the data in the first cell & click ok. Following results are obtained :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Online grades	6	430	71.66666667	226.6666667
Traditional grades	6	445	74.16666667	174.1666667
Hybrid grades	6	480	80	160
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	219.4444444	2	109.7222222	0.58692422	0.56830853	3.682320344
Within Groups	2804.166667	15	186.9444444
Total	3023.611111	17

Conclusion : Since F < F tab, we fail to reject Ho at 5% l.o.s. & thus conclude that there is no significant difference between the mean grades of three groups.

Hope this answers your query!