To solve the problem of finding the point estimate (mean) for the number of cars sold per week for the given sample weeks, we need to follow a few steps. Let's break it down:
1. Identify the Weekly Sales Data:
Here are the weekly sales for the first 26 weeks:
[tex]\[
\{1, 1, 4, 2, 4, 10, 8, 5, 9, 6, 2, 5, 6, 5, 7, 1, 4, \dots\}
\][/tex]
2. Select the Sample Weeks:
The selected sample weeks are: 1, 3, 5, 7, 10, 13, 14, 17, 19, 21.
3. Extract Sales for the Selected Sample Weeks:
We need to extract the sales for each of the selected sample weeks from the given data:
- Week 1: 1 car
- Week 3: 4 cars
- Week 5: 4 cars
- Week 7: 8 cars
- Week 10: 6 cars
- Week 13: 6 cars
- Week 14: 5 cars
- Week 17: 4 cars
- Week 19: The sales data for week 19 and onwards are not provided in the given table, so they will not be considered.
Therefore, the sales data for the sample weeks are: [tex]\([1, 4, 4, 8, 6, 6, 5, 4]\)[/tex].
4. Calculate the Point Estimate (Mean):
The point estimate for the number of cars sold per week is given by the mean of the selected sample sales data:
[tex]\[
\text{Point estimate} = \frac{\sum \text{sample sales}}{\text{number of sample weeks}}
\][/tex]
Summing the sample sales:
[tex]\[
1 + 4 + 4 + 8 + 6 + 6 + 5 + 4 = 38
\][/tex]
Number of sample weeks: 8.
Now, calculate the mean:
[tex]\[
\text{Point estimate} = \frac{38}{8} = 4.75
\][/tex]
Therefore, based on the given sales data and the selected sample weeks, the point estimate for the number of cars sold per week is [tex]\(4.75\)[/tex].
None of the provided multiple-choice answer options (A. 4.8, B. 5.2, C. 6.38, D. 6.1) exactly match the calculated point estimate of [tex]\(4.75\)[/tex]. If you must choose the closest answer, [tex]\(A. 4.8\)[/tex] would be the most appropriate option.
