How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?
A) At α = 0.05, you do not reject H₀.
B) At α = 0.05, you reject H₀.
C) At α = 0.10 you reject H₀.
D) At α = 0.10, you do not reject H₀.

Question

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?
A) At α = 0.05, you do not reject H₀. 
B) At α = 0.05, you reject H₀. 
C) At α = 0.10 you reject H₀. 
D) At α = 0.10, you do not reject H₀.

Quizplus · Accepted Answer

We can use a one-sample t-test to test the hypothesis:

H₀: μ = 60 (the true mean of tissues per cold is 60)
H₁: μ < 60 (the true mean of tissues per cold is less than 60)

The test statistic is calculated as:

t = (x̄ - μ) / (s / sqrt(n)) = (52 - 60) / (22 / sqrt(100)) = -3.64

Using a t-table with 99 degrees of freedom (n-1), at a significance level of α = 0.05 and a one-tailed test, the critical value is -1.660. Since our test statistic is smaller than the critical value, we reject the null hypothesis.

Therefore, the correct decision is to reject H₀ at α = 0.05, which is option B. We have evidence to suggest that the true mean number of tissues used during a cold is less than 60.

How Many Tissues Should the Kimberly Clark Corporation Package of Kleenex