Question

Out of 100 people sampled, 39 preferred Candidate A. Based on this, estimate what proportion of the voting population (pp) prefers Candidate A.

Use a 90% confidence level, and give your answers as decimals, to three places.

___< p <___

Answer 1

Solution :

Given that,

n = 100

x = 39

= x / n = 39 / 100 = 0.39

1 - = 1 - 0.39 = 0.61

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.39 * 0.61) / 100)

= 0.080

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.39 - 0.080 < p < 0.39 + 0.080

0.310 < p < 0.470

(0.310,0.470)

The 90% confidence inerval 0.310 to 0.470