Question 187287: I am having some trouble with my statistics homework. I hope some one can please help.
Hypothesis Testing for the Mean (Large Samples)
Use the guidelines at the end of the project.
1.Convicted murderers receive a sentence of an average of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years. A random sample of 40 cases from the court files from this judge is taken. It is found that sample mean is 17.2 years. Assume that the population standard deviation is 7.4 years. Test at the 0.05 significance level.
a.) Use the critical value z0 method from the normal distribution.
1.H0:
Ha:
2.alpha =
3.Test statistics:
P-value or critical z0 or t0.
4.Rejection Region:
5.Decision:
6.Interpretation:
b) Use the P-value method.
1.H0:
Ha:
2.alpha=
3.Test statistics:
P-value or critical z0 or t0.
4.Rejection Region:
5.Decision:
6.Interpretation:
Hypothesis Testing for Mean (Small Samples)
2. Metro Bank claims that the mean wait time for a teller during peak hours is less than 4 minutes. A random sample of 20 wait times has a mean of 2.6 minutes with a sample standard deviation of 2.1 minutes.
a. Use the critical value z0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance alpha = 0.05. 1.H0 :
Ha :
2.alpha =
3.Test statistics:
P-value or critical z0 or t0.
4.Rejection Region:
5 Decision:
6 Interpretation:
b.) Use the critical value z0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance alpha= 0.01
1.H0 :
Ha :
2.alpha =
3.Test statistics:
4.P-value or critical z0 or t0.
5.Rejection Region:
6.Decision:
7.Interpretation:
I would like to thank you in advance for useing your free time to help me with these problems.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.Convicted murderers receive a sentence of an average of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years.
A random sample of 40 cases from the court files from this judge is taken.
It is found that sample mean is 17.2 years.
Assume that the population standard deviation is 7.4 years.
Test at the 0.05 significance level.
---------------------------------------------
a.) Use the critical value zo method from the normal distribution.
1.Ho: u = 18.7
Ha: u is not equal to 18.7
----------------
2.alpha = 5%
-------------------
3.Test statistics: t(17.2) = (17.2-18.7)/[7.4/sqrt(40)] = -1.2820
---------------------------------
P-value or critical z0 or t0.
4.Rejection Region: t < -2.023 or t > 2.023
-----------------
5.Decision: Since test statistic is not in the reject interval, Fail
to reject Ho.
-----------------
6.Interpretation: The test does not provide strong evidence for rejecting
the belief the average sentence is 18.7
-----------------
b) Use the P-value method.
1.Ho:
Ha:
2.alpha=
3.Test statistics:
---
1,2,3 are the same as above
--------
P-value or critical z0 or t0.
4.Rejection Region:
Same as above.
P-value is 2(P(t < -1.2820) = 2(0.1037) = 0.2074
5.Decision: Since p-value is greater than 5% fail to reject Ho.
6.Interpretation: same as above
--------------------------------------
Hypothesis Testing for Mean (Small Samples)
2. Metro Bank claims that the mean wait time for a teller during peak hours is less than 4 minutes. A random sample of 20 wait times has a mean of 2.6 minutes with a sample standard deviation of 2.1 minutes.
a. Use the critical value z0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance alpha = 0.05.
----------------------
1.Ho: u >= 4 minutes
Ha: u < 4 minutes
------------------------
2.alpha = 5%
------------------
3.Test statistics: t(2.6) = (2.6-4)/[2.1/sqrt(20)] = -2.9814
-----------------------
P-value or critical z0 or t0.
4.Rejection Region: t < -2.093
---
5 Decision: Since -2.9814 is in the reject interval, Reject Ho.
6 Interpretation:
The mean time is not <= 4 minutes
--------------------------------------------
b.) Use the critical value z0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance alpha= 0.01
1.H0 : u <= 4
Ha : u > 4
--------------
2.alpha = 1%
---------------
3.Test statistics: t = 2.9814
4.P-value or critical z0 or t0. p-value = P(t > 2.9814) = 0.0038
--------------
5.Rejection Region:
6.Decision: Since p-value is less than 1% reject Ho
7.Interpretation: same as above.
======================================
Cheers,
Stan H.
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