With individual lines at the checkouts a store manager finds

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on monday mornings is 5.2 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers the waiting times have a standard deviation of 4.3 minutes. Assume that line wiaitng times on monday are normally distributed. Use .05 significance level to test whether the standard deviation of the waiting times using a single line differs from 5.2 minutes. (include hypotheses, test, assumptions, & summary)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   =   5.2  
Ha:    sigma   =/   5.2   [ANSWER, HYPOTHESES]

As the waiting times are normally distributed, we can do the chi^2 test.
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha/2 =    0.025          
df = N - 1 =    28          
chi^2 (crit) =    15.30786055   and   44.46079184  
              
Getting the test statistic, as              
s = sample standard deviation =    4.3          
sigmao = hypothesized standard deviation =    5.2          
n = sample size =    29          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    19.1464497          
              
As chi^2 is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.              

Thus, there is no significant evidence that the standard deviation of the waiting times using a single line differs from 5.2 minutes. [CONCLUSION]