Question

We wish to study the quality of our production line. We take a
random sample of 1000 widgets from our line. A quality rating was
determined for each of the 1000 widgets, and the average quality
rating in the sample was 4. The sample standard deviation was 0.5.
Also, 6 of the 1000 widgets were found to be defective.
Estimate the average quality rating for widgets from our production
line, and include the uncertainty in this estimate in the form, a ± b.

Answer 1

Answer:

(3.9848, 4.0152)

Step-by-step explanation:

Sample size, n=1000

sample mean, $\bar X=4$

Sample S.D= 0.5

Assuming a 95% level of confidence, for this double tailed test, the Z= 0.96

The confidence interval can be computed as;

$(\bar X-Z*\frac{S.D}{\sqrt{n} } ,bar X+Z*\frac{S.D}{\sqrt{n} } )\\\\(4-0.96*\frac{0.5}{\sqrt{1000} } ,4+0.96*\frac{0.5}{\sqrt{1000} } )\\\\(3.9848, 4.0152)$

Therefore from this result, we can say  with 95% certainty that the average quality rating for the widgest lies between 3.9848 and 4.0152