Question

type the correct answer in each box. use numerals instead of words. a company manufactures 2,000 units of its flagship product in a day. the quality control department takes a random sample of 40 units to test for quality. the product is put through a wear - and - tear test to determine the number of days it can last. if the product has a lifespan of less than 26 days, it is considered defective. the table gives the sample data that a quality control manager collected.
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
the point estimate of the population mean is , and the point estimate of the proportion of defective units is .

Explanation:

Step1: Calculate sample mean

The formula for the sample mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 40$ (sample size) and $x_{i}$ are the individual data - points.
$\sum_{i=1}^{40}x_{i}=39 + 31+38 + 40+29+32+33+39+35+32+32+27+30+31+27+30+29+34+36+25+30+32+38+35+40+29+32+31+26+26+32+26+30+40+32+39+37+25+29+34=1240$.
$\bar{x}=\frac{1240}{40}=31$.

Step2: Calculate proportion of defective units

A unit is defective if its lifespan is less than 26 days. Count the number of defective units in the sample. The defective values are 25, 25, so the number of defective units $k = 2$.
The proportion of defective units $\hat{p}=\frac{k}{n}$, where $n = 40$.
$\hat{p}=\frac{2}{40}=0.05$.

Answer:

31, 0.05