Question

A survey of 350 union members in New York State reveals that 63% favor the Republican candidate for governor

a) Construct a 90% confidence interval for the true proportion of all New York State union members who favor the Republican candidate. Round the limits to 3 decimal places.

b) Interpret the interval.

Answer #1

Solution :

Given that,

Point estimate = sample proportion = = 0.63

1 - = 0.37

Z/2 = 1.645

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

= 1.645 * (((0.63 * 0.37) / 350)

= 0.042

**a)** A 90% confidence interval for population
proportion p is ,

- E < p < + E

0.63 - 0.042 < p < 0.63 + 0.042

0.588 < p < 0.672

**b)** We are 90% confidence that interval for the
population proportion p is between 0.588 and 0.672

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