Question

In: Statistics and Probability

Out of 100 people sampled, 39 preferred Candidate A. Based on this, estimate what proportion of...

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 <___

Solutions

Expert Solution

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


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