Question

1. Find the missing values in the following ANOVA Table

Source of Variation	Df	SS	MS	F
Between	3	b	1.56	5.73
Within	a	4.36	c
Total	19

a. What is the total sample size? How many groups are there?

b. If α = 0.025 will you reject Ho? Show your reasoning.

Answer 1

Source of Variation	Df	SS	MS	F
Between	3	1.56*3 = 4.68	1.56	5.73
Within	19-3= 16	4.36	4.36/16 = 0.2725
Total	19

a. What is the total sample size? How many groups are there?

Sample size = df_total + 1 = 19+ 1 = 20

Number of group = df_between + 1 = 3 + 1 = 4

b. If α = 0.025 will you reject Ho? Show your reasoning.

The following is the information provided about the F-distribution numerator and denominator degrees of freedom, and the probability that we need to compute:

Numerator Degrees of Freedom (df1​) =	33
Denominator Degrees of Freedom (df2​) =	1616
Required Probability =	Pr(F≥5.73)

We need to compute Pr(F≥5.73). Using the properties of the cumulative distribution function, the corresponding probability is computed as follows:

Pr(F≥5.73)​=​0.0074​

p = 0.0074

alpha = 0.025

As p < alpha ( 0.0074 < 0.025 )

We reject the null hypothesis