Question

A sample of 52 Elementary Statistics students includes 13 women. Assuming the sample is random. . .

(a) Estimate the percentage of women taking Elementary Statistics with 98% confidence.

(b) At 10% significance, test whether less than 40% of the enrollment in all Elementary Statistics classes consists of women.

(c) If in fact 46% of the students in Elementary Statistics classes are women, find the power of the above test in detecting this parameter.

Answer 1

a) n=52, x=13

p(hat)= 13/52= 0.25

q(hat)= 1-0.25=0.75

Zc for 98% confidence level is 2.33

98% confidence interval is

  is 98% confidence interval.

b) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha= 0.1

The P-Value is 0.013692.The result is significant because p < 0.10.

Decison: Reject Null hypothesis H0

Conclusion: We have sufficient evidence to conclude that less than 40% of the enrollment in all Elementary Statistics classes consists of women.

(c) Power of test=

0.001182891