10. a researcher reports an f - ratio with $df = 4,62$ from an independent - measures research study.
a. how many treatment conditions were compared in the study?
b. what was the total number of participants in the study?
c. use appendix b to find the critical value for f. use $\alpha=.05$.
d. what is the critical region for $\alpha =.01$?

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Recall df between groups formula
For an independent - measures ANOVA, the degrees of freedom between groups (numerator degrees of freedom for the $F$ - ratio) is given by $df_{between}=k - 1$, where $k$ is the number of treatment conditions.
We know that $df_{between} = 4$ (from the $df = 4,62$ where the first value is $df_{between}$ and the second is $df_{within}$).
## Step2: Solve for k
We have the equation $k-1 = 4$.
Adding 1 to both sides of the equation, we get $k=4 + 1=5$.
# Answer: 5

### Part (b)
# Explanation:
## Step1: Recall df within groups formula
For an independent - measures ANOVA, the degrees of freedom within groups (denominator degrees of freedom for the $F$ - ratio) is given by $df_{within}=N - k$, where $N$ is the total number of participants and $k$ is the number of treatment conditions.
We know that $df_{within}=62$ and from part (a) we found that $k = 5$.
## Step2: Solve for N
We have the equation $N - 5=62$.
Adding 5 to both sides of the equation, we get $N=62 + 5 = 67$.
# Answer: 67

### Part (c)
# Explanation:
## Step1: Identify df values
We have $df_{between}=4$ and $df_{within}=62$, and $\alpha = 0.05$.
## Step2: Use F - distribution table
When using the $F$ - distribution table (Appendix B), for $\alpha=0.05$, $df_1 = 4$ (numerator degrees of freedom) and $df_2=62$ (denominator degrees of freedom). Since 62 is not a common value in some tables, we can use the approximation for large $df_2$ or use the table value for $df_2=\infty$ as an approximation (or use a more detailed table). The critical value for $F$ with $df_1 = 4$ and $df_2 = 62$ (or approximated with $df_2=\infty$) at $\alpha = 0.05$ is approximately 2.52 (if we use $df_2 = 60$, the value is 2.52; for $df_2=\infty$, it is 2.41, but a more accurate value using a calculator or a detailed table for $df_2 = 62$ is close to 2.52).
# Answer: Approximately 2.52 (using $df_2 = 60$ as an approximation, the critical value is 2.52)

### Part (d)
# Explanation:
## Step1: Identify df values
We have $df_{between}=4$ and $df_{within}=62$, and $\alpha = 0.01$.
## Step2: Use F - distribution table
When using the $F$ - distribution table (Appendix B), for $\alpha = 0.01$, $df_1=4$ (numerator degrees of freedom) and $df_2 = 62$ (denominator degrees of freedom). Using an approximation (for $df_2 = 60$ as a close value), the critical value for $F$ is approximately 3.67. The critical region is the set of all $F$ - ratios greater than the critical value. So the critical region is $F>3.67$ (if we use $df_2 = 60$; for a more accurate value with $df_2 = 62$, we can calculate or use a calculator, but the approximation with $df_2 = 60$ gives us a critical value of 3.67).
# Answer: The critical region is $F>3.67$ (approximate value, using $df_2 = 60$ as an approximation for $df_2 = 62$)

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Recall df between groups formula

Step2: Solve for k

Step1: Recall df within groups formula

Step2: Solve for N

Step1: Identify df values

Step2: Use F - distribution table

Answer:

Part (b)