Question 3 (11 marks)
According to the Annual survey of drugs expenditure in country X, the annual expenditure for
prescription drugs is $838 per person in the Northeast region of the country. A sample of 60
individuals in the Midwest shows a per person expenditure for prescription drugs of $745. Further, it
is given that the population standard deviation of $300.
a) Formulate hypotheses for a 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 and Identify whether it is a two-tail test or a one tail
test (Left or right tail) (3 marks)
ANSWER:
N (size of sample) = 60
Sample mwean = $745
Standard deviation of population = $300
H0 = μ = $838
Hα = μ < $838
b) Decide the suitable test statistics and justify your selection (1 mark)
ANSWER:
Z = (Sample mean – Population mean) / (Standard deviation / square root of n)
= (745 – 838) / 300 / square root of 60
Z = -2.40
c) Calculate the value of the relevant test statistics and identify the P value (3 marks)
ANSWER:
P value = P(Z<-2.40)
P = 0.0082
d) Based on the p value in part (III), at 99% confidence level, decide the decision criteria (1
mark)
ANSWER:
P value = 0.0082 < α = 0.01
By taking into account outcomit can be stated that alternative hypothesis is true and other one false.
e) Make the final conclusion based on the analysis (3 marks)
ANSWER:
Referring statistical evaluation it can be presented that annual expenditure pertaining to drugs per
person is lower in Midwest as compared to Northeast.
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