Question

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Chapter 9 Reflection:

Annual expenditures for prescription drugs was $838 per person in the Northeast of the country. A sample of 60 individuals in the Midwest showed a per person annual expenditure for prescription drugs of $745. Suppose the population standard deviation is $300. Follow the steps below to develop a hypothesis test to determine whether the sample data support the conclusion that the population annual expenditure for prescription drugs per person is lower in the Midwest than in the Northeast.

1. Formulate the null and alternative hypotheses. State whether this is a one-tailed test (and if so, upper or lower tail) or a two-tailed test.
2. Suppose the significance level is . Explain what this means.
3. Calculate the test statistic. (Hint: Is known or unknown?)
4. Calculate the p-value and make a decision to either reject or to fail to reject .
5. Calculate the critical value(s). Use the test statistic then to make a decision to either reject or to fail to reject .
6. State what your decision means in the context of the problem (prescription expenditure in the Midwest vs. the Northeast).

Answer 1

9.

Given that,
population mean(u)=838
standard deviation, σ =300
sample mean, x =745
number (n)=60
null, Ho: μ=838
alternate, H1: μ<838
level of significance, α = 0.05
from standard normal table,left tailed z α/2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 745-838/(300/sqrt(60)
zo = -2.401
| zo | = 2.401
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =2.401 & | z α | = 1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : left tail - ha : ( p < -2.401 ) = 0.008
hence value of p0.05 > 0.008, here we reject Ho
ANSWERS
---------------
null, Ho: μ=838
alternate, H1: μ<838
test statistic: -2.401
critical value: -1.645
decision: reject Ho
p-value: 0.008
we have enough evidence to support the claim that the population annual expenditure for prescription drugs per person is lower in the Midwest than in the Northeast