Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. nequals​195, xequals​162; ​95% confidence A. 0.778less thanpless than0.883 B. 0.788less thanpless than0.873 C. 0.777less thanpless than0.884 D. 0.789less thanpless than0.873

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 162/195=0.831

1 -   = 1- 0.831 =0.169

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.831*0.169) / 195)

E = 0.053

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.831 - 0.053< p < 0.831 +0.053

0.778< p < 0.883

A. 0.778less thanpless than0.883