Problem 8 (15 points). Two-Sample Hypothesis The results of a mathematics placem
ID: 3324294 • Letter: P
Question
Problem 8 (15 points). Two-Sample Hypothesis The results of a mathematics placement exam at two different campuses of Mercy College follow Campus Sample Size Mean Population Std. Deviation 330 310 31 Answer the following Assume you are trying to conclude that the exam scores at Campus 1 are higher than the exam scores at Campus 2 a. Determine if the appropriate hypothesis test should be an upper tail, lower tail, or 2-tail test b. Determine the value of the test statistic C. Determine the critical z or t value using a level of significance of 5% d. Determine the p-value. e. State your conclusion: Reject Ho or Do not Reject Ho? (Using a significance level of 5%) f. What is the probability of making a Type l Error?Explanation / Answer
Given that,
mean(x)=33
standard deviation , 1 =8
number(n1)=330
y(mean)=31
standard deviation, 2 =7
number(n2)=310
null, Ho: u1 - u2 = 0
alternate, H1: 1 - u2 > 0
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=33-31/sqrt((64/330)+(49/310))
zo =3.37
| zo | =3.37
critical value
the value of |z | at los 0.05% is 1.645
we got |zo | =3.371 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail -Ha : ( p > 3.37 ) = 0.00037
hence value of p0.05 > 0.00037,here we reject Ho
ANSWERS
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a.null, Ho: u1 - u2 = 0
alternate, H1: 1 - u2 > 0 , upper tailed test
test statistic: 3.37
critical value: 1.645
decision: reject Ho
p-value: 0.00037