# Need help with Hypothesis test!!!

#### Zonie987

##### New Member
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.

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
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

#### Zonie987

##### New Member
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
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