Question 9
2 pts
Consider the following hypothesis statement using $a = 0.05$ and data from two independent samples:
Sample characteristics
Sample 1 Sample 2
Variance
3.9
4.5
Size
$30$
We want to test: $H 0 : σ_{1}^{2} = σ_{2}^{2}, H a : σ_{1}^{2} \neq σ_{2}^{2}$ . The test statistic is:
Round your answer to two decimal places.

Answer

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Answer

Find test statistic: $F = 0.82$

Steps

Step 1 ：Calculate F ratio: $F = \frac{σ_{1}^{2}}{σ_{2}^{2}} = \frac{3.9}{4.5}$

Step 2 ：Calculate degrees of freedom: $d_{1} = 30 - 1 = 29, d_{2} = 30 - 1 = 29$

Step 3 ：Find test statistic: $F = 0.82$