Independent random samples were selected from each of two normally distributed populations, $n _ { 1 } = 7$ from population 1 and $n _ { 2 } = 9$ from population 2 . The data are shown below.
$\begin{array} { l l l l l l l l } \text { Population 1: } & 2.5 & 3.1 & 2.3 & 1.8 & 4.2 & 3.5 & 3.9 \end{array}$
$\begin{array} { l l l l l l l l l l } \text { Population 2: } & 2.9 & 1.7 & 4.6 & 3.5 & 3.7 & 2.8 & 4.6 & 3.4 & 1.9 \end{array}$

Find the test statistic for the test of $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } 2$ against $H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$.
A) 1.36
B) .857
C) .735
D) 1.17

Question

Independent random samples were selected from each of two normally distributed populations, $n _ { 1 } = 7$ from population 1 and $n _ { 2 } = 9$ from population 2 . The data are shown below.
$\begin{array} { l l l l l l l l } \text { Population 1: } & 2.5 & 3.1 & 2.3 & 1.8 & 4.2 & 3.5 & 3.9 \end{array}$
$\begin{array} { l l l l l l l l l l } \text { Population 2: } & 2.9 & 1.7 & 4.6 & 3.5 & 3.7 & 2.8 & 4.6 & 3.4 & 1.9 \end{array}$

Find the test statistic for the test of $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } 2$ against $H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$.
A) 1.36
B) .857
C) .735
D) 1.17

Quizplus · Accepted Answer

The test statistic for comparing two variances is calculated using the F-test: $ F = \frac{s_1^2}{s_2^2} $, where $ s_1^2 $ and $ s_2^2 $ are the sample variances. Calculating these from the given data, the test statistic is approximately 1.36.

Independent Random Samples Were Selected from Each of Two Normally n1=7n _ { 1 } = 7n1​=7

Independent Random Samples Were Selected from Each of Two Normally $n _ { 1 } = 7$