To determine the sampling error of the sample, assuming the organization's supposition about the population mean (6.26 days) is correct, follow these steps:
### Step 1: Collect the Data
We have the following data points representing the number of days missed by smokers:
[tex]\[
\begin{array}{rrrrrrrrrrrr}
2 & 0 & 0 & 6 & 12 & 9 & 11 & 5 & 9 & 4 & 11 & 11 \\
8 & 0 & 1 & 4 & 10 & 4 & 2 & 6 & 6 & 11 & 1 & 7 \\
2 & 8 & 1 & 8 & 2 & 6 & 2 & 1 & 4 & 9 & 7 & 5 \\
\end{array}
\][/tex]
### Step 2: Calculate the Sample Mean
To find the sample mean, sum all the data points and then divide by the number of data points.
We sum the data points:
[tex]\[
2 + 0 + 0 + 6 + 12 + 9 + 11 + 5 + 9 + 4 + 11 + 11 + 8 + 0 + 1 + 4 + 10 + 4 + 2 + 6 + 6 + 11 + 1 + 7 + 2 + 8 + 1 + 8 + 2 + 6 + 2 + 1 + 4 + 9 + 7 + 5 = 195
\][/tex]
Next, we count the total number of data points, which is 36.
Thus, the sample mean is:
[tex]\[
\bar{x} = \frac{195}{36} \approx 5.417
\][/tex]
### Step 3: Population Mean
According to the organization's report, the mean number of days missed by smokers is 6.26 days.
### Step 4: Calculate the Sampling Error
The sampling error is the difference between the sample mean and the population mean:
[tex]\[
\text{Sampling Error} = \bar{x} - \mu
\][/tex]
Substituting the values we have:
[tex]\[
\text{Sampling Error} = 5.417 - 6.26 = -0.843
\][/tex]
### Step 5: Present the Final Answer
So, the sample mean and the sampling error are:
[tex]\[
\text{Sample Mean} \approx 5.417
\][/tex]
[tex]\[
\text{Sampling Error} \approx -0.843
\][/tex]
These results indicate that the sample mean is approximately 5.417 days, and the sampling error is approximately -0.843 days.
