Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal places. nequals70?, xequals16?; ?95% confidence A. 0.141less thanpless than0.316 B. 0.130less thanpless than0.327 C. 0.125less thanpless than0.332 D. 0.146less thanpless than0.311

Answer 1

Solution :

Given that,

n = 70

x = 16

= x / n = 16 / 71 = 0.229

1 - = 1 - 0.229 = 0.771

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.229 * 0.771) / 70)

= 0.099

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.229 - 0.099 < p < 0.229 + 0.099

0.130 < p < 0.327

Option B) is correct .