SOLUTION: Please Help! This will be greatly appreciated. (Show Step by step solutions to these problems I got incorrect on my test)Thank You. Question 1 A local bank says that the stan

Question 81325: Please Help! This will be greatly appreciated. (Show Step by step solutions to these problems I got incorrect on my test)Thank You.
Question 1
A local bank says that the standard deviation for bank account balances is less than or equal to $2150.91. A random sample of size n=16 bank accounts reveals a standard deviation of s=$2129.61. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is less than or equal to $2150.91 at the a=0.05 significance level.
Question 2
The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were not equal to the mean scores for Fall 2004 semester. Use a=0.05.
Spring 2004- Test 1= 48.7, Test 2= 68.9,Test 3= 75.2, Test 4= 94.3, Test 5= 98.7
Fall 2004- Test 1= 49.0, Test 2= 68.8, Test 3= 75.5, Test 4= 95.1, Test 5= 100.6
Question 3
An instructor wanted to test the effectiveness of a CALS (Computer Aided Learning System). Two classes were offered in Statistics I. One class used a CALS and the other used traditional methods. At the end of the two courses both classes were given the same final exam. The CALS class had 117 students and 19 of the class receives a grade of B or higher. The class taught using traditional methods had 143 students and 39 of the class receives a grade of B or higher. At a=0.05 can you conclude that the CALS produced a smaller proportion of students with a grade of B or higher.
Question 4
Test the claim that the difference between the mean salary for computer programmers and the mean salary for photographers in Wisconsin is not equal to 28,000. The results of a survey of randomly selected computer programmers and photographers in Wisconsin are shown in the figure below.
Use alpha= 0.01 and Rejection Region test. Testing a Difference other than zero.
Photographers and Computer Programmer Salaries
Computer programmers
x1= $52,400
s1= $8,290
n1= $31
Photographers
x2= $24,200
s2= $3,490
n2= $32

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Question 1
A local bank says that the standard deviation for bank account balances is less than or equal to $2150.91. A random sample of size n=16 bank accounts reveals a standard deviation of s=$2129.61. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is less than or equal to $2150.91 at the a=0.05 significance level.
---------
Ho: sigma <= 2150.91
Ha: sigma > 2150.91
Critical Value Chi-Sq = 32.801
Test Statistic: Chi-Sq = (16-1)2139.61^2/2150.1^2 = 14.84
Conclusion: Fail to Reject Ho
The standard deviation for bank accounts is less than or equal to $2150.91
--------------------

Question 2
The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were not equal to the mean scores for Fall 2004 semester. Use a=0.05.
Spring 2004- Test 1= 48.7, Test 2= 68.9,Test 3= 75.2, Test 4= 94.3, Test 5= 98.7
Fall 2004- Test 1= 49.0, Test 2= 68.8, Test 3= 75.5, Test 4= 95.1, Test 5= 100.6
Ho: mu(spring)-mu(fall)=0
Ha: mu(spring)-to mu(fall) is not equal to zero
Critical Value: t=2.776
mu(spring)=77.16
s(spring)=20.25
mu(fall)=77.8
s(fall)=20.83
s(mu(s)-mu(f))= sqrt[20.25^2/5 + 20.83^2/5]=12.99
Test Statistic: t(mu(f)-mu(s))= [77.8-77.16]/12.99 = 0.049
Fail to Reject Ho
Test results in spring and fall have the same average.
=============
Question 3
An instructor wanted to test the effectiveness of a CALS (Computer Aided Learning System). Two classes were offered in Statistics I. One class used a CALS and the other used traditional methods. At the end of the two courses both classes were given the same final exam. The CALS class had 117 students and 19 of the class receives a grade of B or higher. The class taught using traditional methods had 143 students and 39 of the class receives a grade of B or higher. At a=0.05 can you conclude that the CALS produced a smaller proportion of students with a grade of B or higher.
Ho: p(cals)-p(tm)>=0
Ha: p(cals)-p(tm)<0
Critical value: z=-1.645
Test Stat: z(19/117-39/143)=0.11033/sqrt[(19/117)(98/117)/117+(39/143)(104/143)/143] = -2.185
Conclusion: Reject Ho
CALS results fall below Traditional Methods results
---------------------
Question 4
Test the claim that the difference between the mean salary for computer programmers and the mean salary for photographers in Wisconsin is not equal to 28,000. The results of a survey of randomly selected computer programmers and photographers in Wisconsin are shown in the figure below.
Use alpha= 0.01 and Rejection Region test. Testing a Difference other than zero.
Photographers and Computer Programmer Salaries
Computer programmers
x1= $52,400
s1= $8,290
n1= $31
Photographers
x2= $24,200
s2= $3,490
n2= $32
--------
I'll leave this one to you; I may look at it later or you might
want to post it separately.
Cheers,
Stan H.

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