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
I did it this way and it comes up wrong 1-0.025=0.975/2=.4875 looked up on z chart and got 2.2 +.04=2.24 but that was wrong
To find the critical value for the hypothesis test, you need to determine the appropriate distribution and locate the corresponding value.
In this case, you are comparing two populations (ó1 and ó2) with sample sizes of n1 = 8 and n2 = 10, respectively. Since the population standard deviations are not known, you will need to use the F-distribution.
The F-distribution depends on the degrees of freedom for each sample. For this problem, the degrees of freedom would be (n1-1) and (n2-1).
Degrees of freedom (df1) for the numerator (n1) is equal to 8 - 1 = 7, and degrees of freedom (df2) for the denominator (n2) is equal to 10 - 1 = 9.
You have stated that á (alpha) is 0.025, which is the significance level or the probability of committing a Type I error.
To find the critical value for the F-distribution at the 0.025 level (á = 0.025), you can use statistical software or tables. In this case, you can consult an F-distribution table.
Looking up an F-distribution table with df1 = 7 and df2 = 9, the critical value that corresponds to á = 0.025 is approximately 3.69.
Therefore, the correct critical value for the hypothesis test is 3.69, not 2.24.
It's important to note that the calculation you made using the z-score table is incorrect because the problem involves the F-distribution, not the standard normal distribution (z-score).
Remember to always correctly identify the appropriate distribution and use the corresponding degrees of freedom when determining critical values for hypothesis testing.