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, we do not reject H₀. B) At α = 0.05, we reject H₀. C) At α = 0.05, we accept H₀. D) At α = 0.10, we do not reject H₀.

Question

Quizplus · Accepted Answer

The null hypothesis (HS1U1B10S1U1B0) states that the true mean number of tissues used during a cold is equal to 60. The alternative hypothesis (HA1U1B10S1U1B0) states that the true mean number of tissues used during a cold is less than 60.

We are given a sample mean of 52 and a sample standard deviation of 22. We can use a one-sample t-test to test the null hypothesis at a significance level of α = 0.05.

The test statistic is given by:

t = (x̄ - μ) / (s / sqrt(n))
 
where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (52 - 60) / (22 / sqrt(100)) = -3.64

Using a t-distribution table with 99 degrees of freedom (df = n - 1), we find that the critical value for a one-tailed test with α = 0.05 is -1.66. Since -3.64 is less than -1.66, we reject the null hypothesis and conclude that there is evidence to suggest that the true mean number of tissues used during a cold is less than 60. Therefore, the correct decision is option B, which states that we reject HS1U1B10S1U1B0 at α = 0.05.

How Many Tissues Should the Kimberly Clark Corporation Package of Kleenex