Question

3 0018 Hypothesis testing for Variance and Standard Deviation(Bank ac counts) 417-422 A local bank says that the standard deviation for bank account balances is 2297.94. A random sample of size n 80 bank accounts reveals a standard deviation of s = 2252.88. Assume that the bank balances are nor mally distributed. Test the hypothesis that the standard deviation for bank accounts is not equal to 2297.94 at the a= 0.05 level of significance. Use the Traditional method and refer to the guidelines on page 379 and include the graph. Show the position of the x? critical values and the test statistic. You must number each of the 8 steps on page 379. 15 points (graph is 4 of the 15 points)

Answer 1

Ho :   σ =   2297.94
Ha :   σ ╪   2297.94
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    2252.88
Sample Size ,   n =    80
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    75.9322
      
degree of freedom,   DF=n-1 =    79
Two-Tail Test      
Lower Critical Value   =   56.3089
Upper Critical Value   =   105.473

since, X² lies within critical values, do not reject Ho

there is not enough evidence to conclude that population std dev is different from 2297.94