Question

1. under the null hypothesis of equality of population means, what is the appropriate assumption for the distribution for home prices in the three populations? a) f(2,15) b) f(2,17) c) n(μ,σ) d) t(15)

Explanation:

Step1: Recall the F - distribution in ANOVA

In an ANOVA (Analysis of Variance) test for equality of population means, when the null hypothesis \(H_0:\mu_1=\mu_2=\cdots=\mu_k\) (here \(k = 3\) populations) is True, the test statistic \(F=\frac{MSB}{MSW}\) follows an \(F\) - distribution. The degrees of freedom for the numerator \(df_1=k - 1\) and for the denominator \(df_2=n - k\).

Step2: Calculate degrees of freedom

Given \(k = 3\) (number of populations). Suppose the total number of observations \(n=18\) (since \(df_2=n - k\)). Then \(df_1=k - 1=3 - 1 = 2\) and \(df_2=n - k=18 - 3=15\).

Answer:

A. \(F(2,15)\)