Question

Listen We would like to compare the math proficiency of high school students in different provinces. We take a random sample of five students from each of Canadastes provinces and give them a standardized math test. The mean scores will be compared using an analysis of variance F test. Suppose it is known that scores follow a normal distribution for each of the ten provinces. If we use a 5% level of significance, what is the critical value for the appropriate test?

a 2.03
b 2.08
c 2.12
d 2.83
e 2.64

Answer 1

The critical value for the F test at a 5% level of significance for an ANOVA with 10 groups and 5 observations each (df1=9, df2=40) is typically around 2.83.

Step-by-step explanation:

To determine the critical value for an analysis of variance (ANOVA) F test, we need to consider the degrees of freedom for the numerator (df1) and the denominator (df2). In the given scenario, we have ten provinces and a sample size of five students from each province. Therefore, the degrees of freedom for the numerator (df1) is the number of groups minus one, which is 9 (10 - 1), and the degrees of freedom for the denominator (df2) is the total number of observations minus the number of groups, which is 40 (10 * 5 - 10).

The 5% level of significance indicates that we will look for the critical value in the F-distribution table corresponding to a 95% confidence level. Consulting a standard F-distribution table or using statistical software with the given degrees of freedom, we can find the appropriate critical value. Though the exact critical value is not listed in the provided options, typically for a df1=9 and df2=40, the critical value for F at a 5% significance level is closer to option d, which is 2.83.