The Next Questions Are Based On The Following Information: Suppose that you want to test H 0 = μ = 0.54 against H 1 :μ

Question

The Next Questions Are Based On The Following Information:
Suppose that you want to test H₀= μ = 0.54 against H₁ :μ < 0.54 based on a sample of n = 25 and s = 13.2.
-What is the appropriate critical value?

Quizplus · Accepted Answer

Since the sample size (n) is less than 30 and we don't know the population standard deviation, we need to use a t-distribution for our hypothesis test. The alternative hypothesis is one-tailed (μ < 0.54), so we need to find the critical t-value that corresponds to the α level of significance (the probability of making a Type I error). Using a t-table with degrees of freedom (df) = n-1 = 24 and an α of 0.05 (since the null hypothesis is μ = 0.54 and the alternative is μ < 0.54), we find the critical t-value to be -1.7109. Therefore, the appropriate critical value is -tα/2,n-1 = -t0.05,24 = -1.7109. Choice C is correct.

The Next Questions Are Based on the Following Information