Tests of Hypothesis 
18) The management of White Industries is considering a new method of
assembling its golf cart. The present method requires 42.3 minutes, on the
average, to assemble a cart. The mean assembly time for a random sample of 24
carts, using the new method, was 40.6 minutes, and the standard deviation of
the sample was 2.7 minutes. Using the .10 level of significance, can we
conclude that the assembly time using the new method is faster?


Since the sample was 24, which is less than 30, we must use the t-test,
not the z-test:  

H0: u = 42.3
Ha: u < 43.3

This is a left-tail test.

Calculate the test statistic:
     _
     x - u     40.6 - 42.3 
t = ------- = ------------- = -3.084542639
      s/Vn       2.7/V24

Now we look at the t-table, pasted below. Taking the degrees of 
freedom (df) as 1 less than the number in the sample, or 23, and we find 
the entry I have marked in red below in the table, which is 1.319, 
but we consider it to be -1.319.

The test t-statistic -3.084542639 is well into the rejection
region since it is left of -1.319.  
 
So we reject the hypothesis that the mean with the new method has
not significantly reduced the mean from 42.3. So we assume the new
method is faster.