Question

The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and nurses.

The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and nurses. | School teachers ($) Nurses ($) 845826827875 784 809802 820 829 830 842 832 841 890 821 771 850 859 825829 Is it reasonable to conclude that the mean weekly salary of nurses is higher? Use the .01 significance level. Hint: For the calculations, assume the nurses as the first sample.

This is a  (Click to select)  two  one  -tailed test.
2.	The decision rule is to reject if t is   (Click to select)  greater than  equal to  less than   (Round your answer to 3 decimal places.)
3.	The test statistic is t =  . (Round your answer to 3 decimal places.)
4.	What is your decision regarding (Click to select)  Do not reject.  Reject.
5.	What is the p-value?  (Click to select)  Between 0.01 and 0.1.  Less than 0.001.  Between 0.001 and 0.01.  Greater than 0.1.

Answer 1

Given that,
mean(x)=835.75
standard deviation , s.d1=34.4041
number(n1)=8
y(mean)=826.75
standard deviation, s.d2 =22.8399
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.01
from standard normal table,right tailed t α/2 =2.998
since our test is right-tailed
reject Ho, if to > 2.998
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =835.75-826.75/sqrt((1183.6421/8)+(521.66103/12))
to =0.6505
| to | =0.6505
critical value
the value of |t α| with min (n1-1, n2-1) i.e 7 d.f is 2.998
we got |to| = 0.65049 & | t α | = 2.998
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.6505 ) = 0.26807
hence value of p0.01 < 0.26807,here we do not reject Ho
ANSWERS
---------------
1.
null, Ho: u1 = u2
2.
alternate, H1: u1 > u2
3.
test statistic: 0.6505
critical value: 2.998
4.
decision: do not reject Ho
5.
p-value: 0.26807
p value is Greater than 0.1.
we do not have enough evidence to support the claim that mean weekly salary of nurses is higher
than that of school teachers .