Question

Suppose that a simple random sample of size ?=325 selected from a population has ?=147. Calculate the margin of error for a 95% confidence interval for the proportion of successes for the population, ?p.

Compute the sample proportion, ?̂ ,, standard error estimate, SE, critical value, ?, and the margin of error, ?.. Use a ?-distribution table to determine the critical value. Give all of your answers to three decimal places except give the critical value, ?, to two decimal places.

?̂ =0.452

SE=

Z= 1.96

m=

Answer 1

Solution :

Given that,

n = 325

x = 147

= x / n = 147/ 325 = 0.452

=  0.452

1 - = 1 - 0.452 = 0.548

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

The critical value z = 1.960

Standard error = (( * (1 - )) / n)

= (((0.452 * 0.548) / 325)

= 0.027

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

= 1.960 * (((0.452 * 0.548) / 325)

= 0.052

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.452 - 0.052 < p < 0.452 + 0.052

0.4 < p < 0.504

The 95% confidence interval for the population proportion p is : ( 0.4 , 0.504)

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