Question

In each of the following cases, compute 95 percent, 98 percent, and 99 percent confidence intervals for the population proportion p. (a) pˆ = .8 and n = 97 (Round your answers to 3 decimal places.) 95 percent confidence intervals is [ , ] 98 percent confidence intervals is [ , ] 99 percent confidence intervals is [ , ] (b) pˆ = .5 and n = 312. (Round your answers to 3 decimal places.) 95 percent confidence intervals is [ , ] 98 percent confidence intervals is [ , ] 99 percent confidence intervals is [ , ] (c) pˆ = .7 and n = 118. (Round your answers to 3 decimal places.) 95 percent confidence intervals is [ , ] 98 percent confidence intervals is [ , ] 99 percent confidence intervals is [ , ] (d) pˆ = .1 and n = 51. (Round your answers to 3 decimal places.) 95 percent confidence intervals is [ , ] 98 percent confidence intervals is [ , ] 99 percent confidence intervals is [ , ]

Answer 1

Formula for confidence interval for single population proportions : p

for 95% Confidence level = (100-95)/100 = 0.05 ; /2 = 0.05/2 = 0.025; Z_/2 = Z_0.025 = 1.96

for 98% Confidence level = (100-98)/100 = 0.02 ; /2 = 0.02/2 = 0.01; Z_/2 = Z_0.01 = 2.3263

for 99% Confidence level = (100-99)/100 = 0.01 ; /2 = 0.01/2 = 0.005; Z_/2 = Z_0.005 = 2.5758

(a) pˆ = .8 and n = 97

95 percent confidence intervals

95 percent confidence interval is [0.720, 0.880]

98 percent confidence intervals

98 percent confidence interval is [0.706, 0.894]

99 percent confidence intervals

99 percent confidence interval is [0.695, 0.905]

(b)

pˆ = .5 and n = 312

95% confidence interval

95% confidence interval = [0.445,0.555]

98% confidence interval

98% confidence interval (0.434,0.566)

99% confidence interval

99% confidence interval (0.427,0.573)

(c)

pˆ = .7 and n = 118

95% Confidence interval

95% confidence interval (0.617,0.783)

98% Confidence interval

98% confidence interval  (0.602,0.798)

99% Confidence interval

99% Confidence interval (0.591,0.809)

(d) pˆ = .1 and n = 51

95% Confidence interval

95% confidence interval  (0.018,0.182)

98% Confidence interval

98% confidence interval  (0.002,0.198)

99% Confidence interval

99% Confidence interval (-0.008,0.208)