7.06 Amstat News 2011 reports on a survey of salaries in the United States of fu

Question

7.06 Amstat News 2011 reports on a survey of salaries in the United States of full professors with 6-10 years of service at the given rank. The average salary of 59 statisticians is $168,500 with an estimated standard deviation of $41,480. The average salary of 37 biostatisticians is $188,100 with an esti- mated standard deviation of $41,185. Test whether the mean yearly income of biostatisticians is at least $10,000 greater than the mean income of statis- icns. State the statistical model and hypotheses.

Explanation / Answer

7.06

Given that,
mean(x)=168500
standard deviation , 1 =41480
number(n1)=59
y(mean)=188100
standard deviation, 2 =41185
number(n2)=37
null, Ho: u1 = u2
alternate, H1: 1 < u2
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=168500-188100/sqrt((1720590400/59)+(1696204225/37))
zo =-2.263
| zo | =2.263
critical value
the value of |z | at los 0.05% is 1.645
we got |zo | =2.263 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.263 ) = 0.01181
hence value of p0.05 > 0.01181,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 < u2
test statistic: -2.263
critical value: -1.645
decision: reject Ho
p-value: 0.01181
we have enough evidence to support the income of biostasticians is more than statisticians

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