Business Analytics and Statistics
- The mean of a sample proportion is the same as the population proportion.
The population proportion (p) is x/n
Where x is the population of defective items
Therefore p = 25/500= 0.05
Since p = 0.05, then µ= 0.05
The calculation of the confidence interval depends on the mean and standard deviation of the proportion from sampling distribution (Albright & Winston, 2016). However, since the population parameter is unknown, a sample proportion is appropriate for the estimate.
Sp= √p(1-p)/N
= √0.05(1-0.05)/500
=0.00975
Since the population proportion is assumed as binomial, the confidence interval is given, as shown below.
p- Zα Sp ≤p≤ p+ Zα Sp
From the normal probability table, the confidence interval of 95% is 1.96
0.05-1.96(0.00975)≤p≤0.05+1.96(0.00975)
0.03089≤p≤0.06911
- There is a 95% confidence that the mean proportion of defective items falls between 0.03089 and 0.06911
- Population mean is µ±1.96∂/√n
0.05±1.96(0.00975)/√500= 0.05±0.000854
0.050854, 0.049146
The actual population mean falls within the constructed confidence interval.
475 of the constructed intervals should include the true population mean.
Reference
Albright, S. C., & Winston, W. L. (2016). Business analytics: Data analysis and decision making. Boston, MA: Cengage Learning.