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

Answer:

$t_{critical} \text{ at 0.01 level of significance, 100 degree of freedom} = -2.364$              

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 20 ounces

Sample size, n = 101

Alpha, α = 0.01

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 20\text{ ounces}\\H_A: \mu < 20\text{ ounces}$

We use one-tailed t test to perform this hypothesis.

$t_{stat} = -2.89$

Now,

$t_{critical} \text{ at 0.01 level of significance, 100 degree of freedom} = -2.364$

Conclusion:

Since the calculated test statistic is less than the critical value we fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis.

Thus, there is enough evidence to support the claim that the mean amount of beverage in a medium drink sold at this college's cafeteria is less than 20 ounces