Let's go through the solution step-by-step to find the point estimate for the number of cars sold per week for the given sample of weeks: 1, 3, 5, 7, 10, 13, 14, 17, 19, and 21.
1. Given Data:
- Weekly car sales for the first 8 weeks:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Week} & \text{Cars Sold} \\
\hline 1 & 1 \\
\hline 2 & 1 \\
\hline 3 & 4 \\
\hline 4 & 2 \\
\hline 5 & 4 \\
\hline 6 & 10 \\
\hline 7 & 8 \\
\hline 8 & 5 \\
\hline
\end{array}
\][/tex]
2. Identify the Cars Sold in the Selected Weeks:
- Weeks in our sample are: 1, 3, 5, and 7. (Since data for the other weeks 10, 13, 14, 17, 19, and 21 are not available.)
- Number of cars sold in these selected weeks:
- Week 1: 1 car
- Week 3: 4 cars
- Week 5: 4 cars
- Week 7: 8 cars
3. Calculate the Total Number of Cars Sold in the Selected Weeks:
- Sum the cars sold in weeks 1, 3, 5, and 7:
[tex]\[
1 + 4 + 4 + 8 = 17 \text{ cars}
\][/tex]
4. Determine the Number of Sample Weeks:
- Total number of sample weeks is 10, as listed: 1, 3, 5, 7, 10, 13, 14, 17, 19, and 21.
5. Calculate the Point Estimate:
- The point estimate for the number of cars sold per week is given by:
[tex]\[
\text{Point Estimate} = \frac{\text{Total Cars Sold in Sample Weeks}}{\text{Total Number of Sample Weeks}}
\][/tex]
- Substituting the values:
[tex]\[
\text{Point Estimate} = \frac{17}{10} = 1.7
\][/tex]
Answer:
The point estimate for the number of cars sold per week for the given sample is 1.7 cars per week. This corresponds to none of the provided choices A, B, C, or D.
