In: Statistics and Probability
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.
Given:
= $838, n = 60, = $745, = $300
Hypothesis:
Ho: = $838
Ha: < $838 (One tailed test, Lower tail)
Significance level () = 0.05
Test
statistic: Population
standard deviation ()
is Known, So We can use Z test
P-value: 0.0082 ...................Using standard Normal table
Conclusion:
P-value < , i.e. 0.0082 < 0.05, That is Reject Ho at 5% level of significance.
Critical value:
Z =Z0.05 = -1.645 ..................Using standard Normal table
Conclusion:
Z < Z , i.e. -2.40 < -1.645, That is Reject Ho at 5% level of significance.
Therefore, 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.