Question

A random sample of male employees is taken at the end of a year and the mean
number of hours of absenteeism for the year is found to be 63 hours. A similar
sample of 50 female employees has a mean of 66 hours. Could these samples be
drawn from a population with the same mean and standard deviation of 10 hours?
(Use α = 5%)

Answer 1

We will apply the students t test :  Independent two sample test.
Size of each sample :  n = 50    
Assume std deviation of the two samples =
         std deviation of the population = s = 10 hours 
X1 = mean of first sample = 63 hrs 
X2 = mean of 2nd sample = 66 hrs
Confidence level expected = 1 - α =  95%

student's t = (X2 - X1) /[s √(2/n) ] = (66 - 63) / [ 10 √(2/50) ] 
                 = 1.5

Degrees of freedom = size of sample1  - 1 + size of sample2 - 1
            = 98

From the t- distribution table with two sided values for probability and 100 deg of freedom:
   P (-1.66 < t < 1.66) = 0.90
So  P( -1.5 < t < 1.5)  < 0.90

Hence, the confidence level is less than 90% to say that the given samples belong to the same population with the same mean.

So answer is NO  for  α = 5%.