To calculate the point estimate of the population mean, we need to determine the average lifespan of the sample data provided. The sample data consists of the following 40 values:
[tex]\[ 39, 31, 38, 40, 29, 32, 33, 39, 35, 32, 32, 27, 30, 31, 27, 30, 29, 34, 36, 25, 30, 32, 38, 35, 40, 29, 32, 31, 26, 26, 32, 26, 30, 40, 32, 39, 37, 25, 29, 34 \][/tex]
We calculate the mean (average) of these values to obtain the point estimate of the population mean.
The point estimate of the population mean is 32.3.
To find the point estimate of the proportion of defective units, we need to count how many of the units in the sample have a lifespan of less than 26 days.
From the sample data provided, the units with a lifespan less than 26 days are:
[tex]\[ 25, 25 \][/tex]
There are 2 defective units out of the 40 sampled units.
The proportion of defective units is:
[tex]\[
\frac{\text{Number of defective units}}{\text{Total number of units}} = \frac{2}{40} = 0.05
\][/tex]
Therefore, the point estimate of the proportion of defective units is 0.05.
