Question

In: Statistics and Probability

How diverse are TXST employees when it comes to race and ethnicity? In a random sample...

How diverse are TXST employees when it comes to race and ethnicity? In a random sample of 100 TXST employees, 26 were racial or ethnic minorities.
1. Using a calculator, report a 95% confidence interval for the population proportion of all TXST employees who are racial or ethnic minorities.

b. Interpret the 95% confidence interval you constructed.

Expert Solution

Solution :

Given that,

n = 100

x = 26

Point estimate = sample proportion = = x / n = 26/1000.26

1 - = 1- 0.26 =0.74

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.26*0.74) /100 )

E = 0.0860

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.26-0.0860< p < 0.26+0.0860

0.1740< p < 0.3460

The 95% confidence interval for the population proportion p is : 0.1740,0.3460

orchestra answered 2 years ago

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