Question

A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.

		0.308 < p < 0.438
		0.304 < p < 0.442
		0.301 < p < 0.445
		0.316 < p < 0.430

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 112 / 300 = 0.373

1 - = 1 - 0.373 = 0.627

Z/2 = 2.326

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

= 2.326 * (((0.373 * 0.627) / 300)

Margin of error = E = 0.065

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.373 - 0.065 < p < 0.373 + 0.065

0.308 < p < 0.438

The 98% confidence interval for the population proportion p is : 0.308 , 0.438