Need help with Hypothesis test!!!

#1
Okay I can't seem to figure out this problem. Would really appreciate any help that can be given.

A sample of 81 account balances of a credt company showed an average balance of $1,200 with a standard deviation of $126. You want to determine if the mean of all account balances si significantly different from $1150. Use a .05 level of confidence.

A) State the null hypothesis
B) WHat is the rejection rule?
C) COmpute the value of the test statitstic z.
D) What is your conclusion?

This is what I have come up with so far. Not sure if its right, but I gave it a try.

A) Ho: µ = 1150
Ha: µ ≠ 1150

B) Ho is rejected when z > 1.64

C) Sample size: 81
Mean: 1200
Std Dev: 126

Hypothesized value: 1150

Standard error: 14
Test statistic z: 3.571428571

D) Since z >1.64 Ho will be rejected.
 
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JohnM

TS Contributor
#2
Of course you can figure it out - you were very close! :tup:

B) z should be +/- 1.96
since it is a two-tailed test (Ha includes a ≠ sign), the rejection region of .05 is divided between the two tails, so the z value will be larger

C) z = (1150 - 1200) / (126/sqrt(81)) = -3.571

D) since -3.571 is < -1.96, reject Ho
 
#3
Okay I think I understand most of it, but shouldn't the equation for Z be : (1200-1150)/ (126/sqrt(81)) = -3.571.

That would be subtracting the Hypothesized value from the sample mean? Which would cause the z value to be positive?
 

JohnM

TS Contributor
#4
the equation for z is always:

(x - mu) / s

or

(x - mu) / (s/sqrt(n))

it's always the sample mean minus the hypothesized mean