Question

Choose the best answer.
Find and interpret a 95% confidence interval for a population mean μ for these values:
A. n = 36, x̄ = 13.1, s² = 3.42
B. n = 64, x̄ = 2.73, s² = .1047

Select one:

A. 13.1 ± 0.1007
B. 2.73 ± 0.0099

A. 13.1 ± 0.1862
B. 2.73 ± 0.0032

A. 13.1 ± 1.1172
B. 2.73 ± 0.0257

A. 13.1 ± 0.6041
B. 2.73 ± 0.0793

Answer 1

A.

n=36

xbar= 13.1

variance= 3.42

Thus, sd= sqrt(variance)

= sqrt(3.42)

= 1.849324

At 95% confidence, the Z value is 1.96. ( + and - )

Thus, confidence interval

= xbar - Z *s / sqrt(n) , xbar + Z *s / sqrt(n)

= 13.1 - 1.96 * 1.849324 / sqrt(36) ,  13.1 + 1.96 * 1.849324 / sqrt(36)

= 13.1 - 1.96 * 0.3082207 , 13.1 + 1.96 * 0.3082207

= 13.1 - 0.6041126 , 13.1 + 0.6041126

= 12.49589, 13.70411

B.

n=64

xbar= 2.73

variance= 0.1047

Thus, sd= sqrt(variance)

= sqrt(0.1047)

= 0.3235738

At 95% confidence, the Z value is 1.96. ( + and - )

Thus, confidence interval

= xbar - Z *s / sqrt(n) , xbar + Z *s / sqrt(n)

= 2.73 - 1.96 * 0.3235738 / sqrt(64) ,  2.73 + 1.96 * 0.3235738 / sqrt(64)

= 2.73 - 1.96 * 0.04044673 , 2.73 + 1.96 * 0.04044673

= 2.73 - 0.07927559 , 2.73 + 0.07927559

= 2.650724, 2.809276

Thus, the correct answer is the last option.