Question

Find the critical value(s) that would be used in a hypothesis test of the following claim. Claim: "The mean amount of beverage in a medium drink sold at this college's cafeteria is less than 20 ounces." A random sample of 101 medium drinks from this cafeteria is collected, and it produces a test statistic of t = -2.89. A significance level of α = 0.01 is to be used.

Answer 1

To find the critical value(s) for the hypothesis test, use the t-distribution and the given significance level α = 0.01. The critical value is approximately -2.617.

Step-by-step explanation:

To find the critical value(s) that would be used in a hypothesis test of the claim, we need to use the t-distribution and the given significance level α = 0.01. Since the claim is that the mean amount of beverage is less than 20 ounces, this is a left-tailed test.

First, we need to find the degrees of freedom (df) which is equal to the sample size minus 1, so df = 101 - 1 = 100.

Next, we find the critical value by looking up the upper-tail probability of α = 0.01 and the degrees of freedom of 100 in the t-distribution table. The critical value is approximately -2.617.