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: x = 52, s = 22. suppose the test statistic does fall in the rejection region at α = 0.05. which of the following conclusion is correct? how many tissues should the kimberly clark corporation package of kleenex contain?

O at α = 0.05, there is insufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.
O at α = 0.05, there is not sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
O at α = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
O at α = 0.10, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

Answer 1

At α = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

Step-by-step explanation:

The question asks for the correct conclusion based on the test statistic falling in the rejection region at a significance level of α = 0.05. The given data includes the sample mean (x) of 52, the sample standard deviation (s) of 22, and the hypothesized population mean (μ) of 60. To determine the correct conclusion, we need to perform a hypothesis test.

Step-by-step:

1. State the null hypothesis (H0): The mean number of tissues used during a cold is 60.
2. State the alternative hypothesis (H1): The mean number of tissues used during a cold is not 60.
3. Calculate the test statistic using the formula: t = (x - μ) / (s / √n), where n is the sample size. In this case, n = 100.
4. Determine the critical value(s) based on the significance level (α = 0.05) and the degrees of freedom (df = n - 1 = 99). We can use a t-distribution table or statistical software to find the critical value.
5. Compare the test statistic to the critical value(s). If the test statistic falls in the rejection region, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
6. Based on the comparison, we can conclude that at α = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.