The math department has a standard final for Mat131 classes It is known that the average student score on this final is an 80, with a standard deviation of 8.5 points. Mr Goodteather just graded the final exams for 18 of his students and had an average score of 85. Mr. Badteacher graded the final exams for 29 of his students and had an average score of 78. Each teacher has over 100 Mat131 students so these grades are only samples. An administrator saw these results and decided 2 things:1) Mr. Goodteacher\'s students do better than average so he must be a good teacher and 2) Mr Badteacher\'s students do worse than average so he must not be a good teacher. Is there sufficient evidence to show that either, neither, or both of those conclusions are true? A) If the administrator wanted to quickly judge each teacher by taking 5 sample from each to see if any had average scores higher than the overall college\'s average score, what would the averge of those 5 sample tests at least need to be for it to be significant at the .05level? Show all work Solution 1) population mean,u=80 population standard deviation,s = 8.5 alpha,a=0.05 a. sample size,n1=18 sample mean,x1=85 H0: u=80 H1: u>80 b. test statistic, z = (x1-u) / (s/sqrt(n1)) z = 2.496 critical value = Za = Z0.05 = 1.645 since z>1.645 hence reject H0 So, we conclude that Mr. Goodteacher\'s students do better than average so he must be a good teacher the administrator\'s claim about Mr. Goodteacher is valid. 2) population mean,u=80 population standard deviation,s = 8.5 alpha,a=0.05 a. sample size,n1=29 sample mean,x1=78 H0: u=80 H1: u<80 b. test statistic, z = (x1-u) / (s/sqrt(n1)) z = -1.267 critical value = -Za = -Z0.05 = -1.645 since z> -1.645 hence H0 can not be rejected So, there is no sufficient evidence to show that Mr Badteacher\'s students do worse than average the administrator\'s claim about Mr Badteacher is NOT valid.

1. The math department has a standard final for Mat131 classes It is known that the average
student score on this final is an 80, with a standard deviation of 8.5 points. Mr Goodteather just
graded the final exams for 18 of his students and had an average score of 85. Mr. Badteacher
graded the final exams for 29 of his students and had an average score of 78. Each teacher has
over 100 Mat131 students so these grades are only samples. An administrator saw these results
and decided 2 things:1) Mr. Goodteacher's students do better than average so he must be a good
teacher and 2) Mr Badteacher's students do worse than average so he must not be a good
teacher. Is there sufficient evidence to show that either, neither, or both of those conclusions are
true?
A) If the administrator wanted to quickly judge each teacher by taking 5 sample from each to see
if any had average scores higher than the overall college's average score, what would the averge
of those 5 sample tests at least need to be for it to be significant at the .05level?
Show all work
Solution
1)
population mean,u=80
population standard deviation,s = 8.5
alpha,a=0.05
a.
sample size,n1=18
sample mean,x1=85
H0: u=80
H1: u>80
b.
test statistic, z = (x1-u) / (s/sqrt(n1))
z = 2.496
critical value = Za = Z0.05 = 1.645
since z>1.645 hence reject H0
So, we conclude that Mr. Goodteacher's students do better than average so he must be a good

2. teacher
the administrator's claim about Mr. Goodteacher is valid.
2)
population mean,u=80
population standard deviation,s = 8.5
alpha,a=0.05
a.
sample size,n1=29
sample mean,x1=78
H0: u=80
H1: u<80
b.
test statistic, z = (x1-u) / (s/sqrt(n1))
z = -1.267
critical value = -Za = -Z0.05 = -1.645
since z> -1.645 hence H0 can not be rejected
So, there is no sufficient evidence to show that Mr Badteacher's students do worse than average
the administrator's claim about Mr Badteacher is NOT valid