Find the critical value for the hypothesis test, given the following. (Give your answer correct to two decimal places.)
Ha: ó1 > ó2, with n1 = 8, n2 = 10, and á = 0.025
F = 2.24 is what I got .
To find the critical value for a hypothesis test with the given information, we need to use the F-distribution. The F-distribution is used when comparing the variances of two populations.
In this case, the null hypothesis (Ho) is that the variance of population 1 (ó1) is less than or equal to the variance of population 2 (ó2). The alternative hypothesis (Ha) is that the variance of population 1 (ó1) is greater than the variance of population 2 (ó2).
Since we have a one-sided test (Ha: ó1 > ó2), we need to find the critical value in the upper tail of the F-distribution.
To find the critical value, we can use the F-distribution table or a calculator. Here's how you can use a calculator:
1. Open a calculator or statistical software that has the F-distribution feature.
2. Enter the degrees of freedom for each sample (n1-1 = 8-1 = 7, n2-1 = 10-1 = 9) and the significance level (á = 0.025).
3. Choose the option to find the critical value for the right tail (upper tail) of the F-distribution.
4. Calculate the critical value.
Using this approach, the critical value turns out to be approximately 3.42 when rounded to two decimal places.
Therefore, the correct critical value for this hypothesis test is 3.42, not 2.24.