Question

In a random sample of 80 people, 52 consider themselves as baseball fans. Compute a 92% confidence interval for the true proportion of people consider themselves as baseball fans and fill in the blanks appropriately. We are 92% confident that the true proportion of people consider themselves as baseball fans is between_____ and _______.

Answer 1

Solution :

Given that,

n = 80

x = 52

Point estimate = sample proportion = = x / n = 52/80=0.65

1 - = 1-0.65=0.35

At 92% confidence level

= 1 - 92%  

= 1 - 0.92 =0.08

/2 = 0.04

Z/2 = Z0.04= 1.75 ( Using z table )   

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

= 1.75 (((0.65*0.35) / 80)

E = 0.0933

A 92% confidence interval for population proportion p is ,

- E < p < + E

0.65-0.0933 < p <0.65+ 0.0933

0.5567< p < 0.7433

The 92% confidence interval for the population proportion p is : 0.5567,0.7433