To determine the point estimate of the population mean lifespan of the product, we use the sample data provided. The population mean is estimated by calculating the average (mean) of the sample data.
Given the sample data:
[tex]\[
\begin{aligned}
&39, 31, 38, 40, 29 \\
&32, 33, 39, 35, 32 \\
&32, 27, 30, 31, 27 \\
&30, 29, 34, 36, 25 \\
&30, 32, 38, 35, 40 \\
&29, 32, 31, 26, 26 \\
&32, 26, 30, 40, 32 \\
&39, 37, 25, 29, 34 \\
\end{aligned}
\][/tex]
The point estimate of the proportion of defective units is determined by counting the number of units in the sample that are considered defective (i.e., with a lifespan of less than 26 days) and dividing it by the total number of units in the sample.
The calculated values are as follows:
- The point estimate of the population mean is [tex]\( 32.3 \)[/tex].
- The point estimate of the proportion of defective units is [tex]\( 0.05 \)[/tex].
So, the point estimate of the population mean is [tex]\( 32.3 \)[/tex], and the point estimate of the proportion of defective units is [tex]\( 0.05 \)[/tex].
