Hypothesis help

Question

I have a hard time interpreting my results and I need help with the rejection method.

A local bank claims that the standard deviation of the checking account balances of its customers is $275. A random sample of 41 accounts were checked and the standard deviation was $263.35. Using the method of your choice (P-value or rejection), test the hypotheses using a level of significance of 0.01. What is your decision regarding the null hypothesis?
Null µ = 275Alternative µ ≠ 275
Test Statistic = 36.683
Lower Rejection Region = 22.16426
Upper Rejection Region= 63.69073975
Should I reject or fail to reject?
Also, should I support the banks claim?

Answer 1

John,

 

Based on what you've indicated, you would NOT reject the null hypothesis (that the SD = $275).

 

The numbers provided for both the lower and upper rejection regions are threshold values (on a normal distribution).  If the test statistic is either greater than the upper threshold or less than the lower threshold, then the null hypothesis would be rejected.

 

Since 36.68 lies between the two, it does not fit the criteria for rejection.  

 

Yes, you should support the bank's claim.

 

BTW, the notation used in the question typically refers to the mean (μ = 275), not the standard deviation.