Question

A   national   business   magazine   reports   that   the   mean   age   of   retirement   for   women   executives   is   61.0.       A   women’s   rights   organization   believes   that   this   value   does   not   accurately   depict   the   current   trend   in   retirement.       To   test   this,   the   group   polled   a   simple   random   sample   of   95   recently   retired   women   executives   and   found   that   they   had   a   mean   age   of   retirement   of   61.5.       Assuming   the   population   standard   deviation   is   2.5   years,   is   there   sufficient   evidence   to   support   the   organization’s   belief   at   the       ?=0.05   significance   level?  
  

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 61
Alternative Hypothesis: μ ≠ 61

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (61.5 - 61)/(2.5/sqrt(95))
z = 1.95

P-value Approach
P-value = 0.0512
As P-value >= 0.05, fail to reject null hypothesis.

Rejection Region Approach
As the value of test statistic, z is within critical value range, fail to reject the null hypothesis