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: X = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decision 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 do not reject H₀.
D) At α = 0.10, you reject H₀.

Question

Quizplus · Accepted Answer

We need to perform a one-sample t-test with the following hypotheses:
H₀: μ = 60 (the true mean number of tissues used during a cold is 60)
H₁: μ ≠ 60 (the true mean number of tissues used during a cold is not 60)

The sample mean is X̄ = 52 and the sample standard deviation is S = 22. The sample size is n = 100 and the degrees of freedom are df = n - 1 = 99.

The t-score is calculated as:
t = (X̄ - μ) / (S / sqrt(n)) = (52 - 60) / (22 / sqrt(100)) = -3.64

At α = 0.05, the critical values for a two-tailed test with 99 degrees of freedom are ±1.984. Since the absolute value of the t-score (3.64) is greater than the critical value (1.984), we reject the null hypothesis.

Therefore, the correct decision is to reject H₀ at α = 0.05, which is option B.

How Many Tissues Should the Kimberly Clark Corporation Package of Kleenex