SOLUTION: Hi, can you please explain the steps (formulas) "in detail" of finding the p-value uaing a z-test, and a one tailed test and a two tailed test. Ex: z= 1764 -1750/ 70/ sqrt 15

Question 181239: Hi,
can you please explain the steps (formulas) "in detail" of finding the p-value uaing a z-test, and a one tailed test and a two tailed test.
Ex: z= 1764 -1750/ 70/ sqrt 150 = 2.4494 ~ 2.449
Also how do you find a critical value, do you follow the same steps?
I have this example but I don't understand where 0.937 came from or what the P is and why there are the <= symbols when doing addition?:
=P(Z<= -1.531) + P(Z>= 1.531)
=P (Z<= -1.531)+ (1-P(Z< 1.531))
=0.063 + (1-0,937)
=0.126
Thank you

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
can you please explain the steps (formulas) "in detail" of finding the p-value uaing a z-test, and a one tailed test and a two tailed test.
---------------------
Formula for test statistic: z((x-bar)-u) = ((x-bar)-u)/sqrt[s/sqrt(n)}
Ex: z= (1764 -1750)/[ 70/ sqrt 150] = 2.4494 ~ 2.449
-----------------
If this is a 2-tail test p-value = 2*P(z>2.449) = 2*0.00716 = 0.1433..
If this is a right-tail test p-value = P(z>2.449) = 0.00716
---------------------------------------------
Comment: This p-value business is an alternative to comparing the
position of the test statistic to the position of the critical value.
If the test statistic is not in the rejection interval the p-value
will be greater than alpha; If the test statistic is in the rejection
interval the p-value will be less than alpha.
You can see this if you draw a normal curve, select a z=critical value
like 1.645 then, arbitrarily place a test-statistic value in the
critical interval or outside the critical interval. For a right tail
test the area to the right of the critical value is alpha, If the
test-statistic is in the reject interval the area to the right of the
test-statistic will be less than alpha. That area to the right of
the test-statistic is the P-value. So if you know the p-value is less
than alpha you automatically know the test statistic is in the reject
interval and you Reject Ho.
------------------------------------------------
Also how do you find a critical value, do you follow the same steps?
A two-tail test with alpha = 5% results in critical values of +1.96
and -1.96. (1/2)of alpha is to the right of 1.96 and (1/2) of alpha
is to the left of -1.96. You need a calculator or a z-table to determine
these critical values.
-----------------------------------
I have this example but I don't understand where 0.937 came from or what the P is and why there are the <= symbols when doing addition?:
=P(Z<= -1.531) + P(Z>= 1.531)
=P (Z<= -1.531)+ (1-P(Z< 1.531))
=0.063 + (1-0,937)
=0.126
---------
I looks like you are determining the p-value for a two-tail test.
The test statistic turned out to be 1.531
The p-value is P(z<=-1.531) + P(z>=1.531)
-------------------------
Note: This is the same as 2*P(z>1.531) because the area to the right
of z=1.531 is the same as the area to the left of z=-1.531.
--------------------------------
The area to the left is 0.063.
The area to the right is 1-the area above z=1.531 which is also 0.063.
Adding the two you get 2(0.063) = 0.126
===============================================
Hope this helps.
Cheers,
Stan H.
-------------

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