Question

A university believes that the average retirement age among the faculty is now 70 instead of the historical value of 65. A sample of 35 faculty found that the average of their expected retirement age is 68.4 with a standard deviation of 3.6. Conduct the appropriate hypothesis test to determine if the mean retirement age is not equal to 70.

Round your final answer to four decimal places. 0.0000

Answer 1

SOLUTION:

From given data,

A university believes that the average retirement age among the faculty is now 70 instead of the historical value of 65. A sample of 35 faculty found that the average of their expected retirement age is 68.4 with a standard deviation of 3.6. Conduct the appropriate hypothesis test to determine if the mean retirement age is not equal to 70.

Where,

Population mean = = 70

Sample mean = = 68.4

Sample size = n = 35

Sample Standard deviation = =3.6

Significance level = = 0.05

Test hypothesis:

: = 70 (Null hypothesis)

: 70 (Alternative hypothesis)

The test statistic is,

t = ( - ) / ( / sqrt(n))

t = (68.4 - 70) / (3.6 / sqrt(35))

t = -1.6 / 0.60851106

t = - 2.629

Degree of freedom

df = n-1 = 35-1 = 34

P-value :

P-value = P (t < - 2.629 ) = 0.0130

Conclusion:

Where,

P-value = 0.0130 < Significance level = = 0.05 then we reject null hypothesis