Question

2018 Hypothesis testing for Variance and Standard Deviation(Bank ac counts) 417-422 local bank says that the standard deviation for bank account balances is 2338.16. A random sample of size bank accounts reveals a standard deviation of s = 2226.82. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is greater than or equal to 2338.16 at the 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 statistie. You must number each of the 8 steps on page 379. 15 points (graph is 4 of the 15 points)

Answer 1

Ans:

Left tailed test.

Ho :σ Σ 2338.16

H:0 < 2338.16

n=90

s=2226.82

Test statistic:

Chi square=(90-1)*2226.82^2/2338.16^2=80.726

df=90-1=89

critical chi square(left tailed)=CHIINV(0.95,89)=68.249

p = 0.05 as 48.98 a se _89 _6232 ._T5,66 1 x2 - 68.24 _823_111_ _1023 1151 29 _

As,chi square test statistic does not lie in rejection region,we fail to reject the null hypothesis.