Please answer both questions thouroughly. Thank you! 1. A college student is inv
ID: 3310209 • Letter: P
Question
Please answer both questions thouroughly. Thank you!
1. A college student is investigating the claim that students who graduate with a master's degree earn higher salaries, on average, than those who finish with a bachelor's degree. She surveys, at random, 42 recent graduates with master's degrees and finds that their mean salary is $38,400/yr. The standard deviation of salaries for those with master's degrees is $3100. She also surveys, at random, 45 recent graduates with bachelor's degrees and finds their mean salary is $36,750/yr. The standard deviation of salaries for those with bachelor's degrees is $3700. Test the claim at a 0.05 level of significance 2. A professor believes that, for the introductory art history classes at his university, the mean test score of students in the evening classes is more than 5 points lower than the mean test score of students in the morning classes. He collects data from a random sample of 250 students in evening classes and finds that they have a mean test score of 80.2. He knows the population standard deviation for the evening classes to be 11.9. A random sample of 300 students from morning classes results in a mean test score of 86.8. He knows the population standard deviation for the morning classes to be 10.2 points. Test his calm with a 95% level of confidenceExplanation / Answer
Q1.
Given that,
mean(x)=38400
standard deviation , s.d1=3100
number(n1)=42
y(mean)=36750
standard deviation, s.d2 =3700
number(n2)=45
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.683
since our test is right-tailed
reject Ho, if to > 1.683
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =38400-36750/sqrt((9610000/42)+(13690000/45))
to =2.26
| to | =2.26
critical value
the value of |t | with min (n1-1, n2-1) i.e 41 d.f is 1.683
we got |to| = 2.25999 & | t | = 1.683
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 2.26 ) = 0.0146
hence value of p0.05 > 0.0146,here we reject Ho
ANSWERS
---------------
null, Ho: u1 < u2
alternate, H1: u1 > u2
test statistic: 2.26
critical value: 1.683
decision: reject Ho
p-value: 0.0146
we have evidence to support that Msater degree student will paid highest