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: mean= 55, S = 20. Using the sample information provided, calculate the value of the test statistic.

Answer 1

To calculate the test statistic for this scenario, we will use the formula for the t-test statistic:

\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]

Where:
- \(\bar{x}\) = sample mean
- \(\mu\) = population mean (hypothesized mean)
- \(s\) = sample standard deviation
- \(n\) = sample size

From the information given:
- Sample mean (\(\bar{x}\)) = 55
- Hypothesized mean (\(\mu\)) = 60
- Sample standard deviation (\(s\)) = 20
- Sample size (\(n\)) = 100

Now, we can plug in the values into the formula.

First, calculate the standard error (SE):

\[
SE = \frac{s}{\sqrt{n}} = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2
\]

Next, calculate the test statistic \(t\):

\[
t = \frac{55 - 60}{2} = \frac{-5}{2} = -2.5
\]

Thus, the value of the test statistic is:

\[
\boxed{-2.5}
\]