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Statistics

Business Analytics and Statistics

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Business Analytics and Statistics

  1. 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

  1. There is a 95% confidence that the mean proportion of defective items falls between 0.03089 and 0.06911
  2. 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.

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