Question

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. Show your work.

2. Suppose the significance level is a = .05. Explain what this means. Show your work.

3. Calculate the test statistic. (Hint: Is σ known or unknown?) Show your work.

4. Calculate the p-value and make a decision to either reject H₀  or to fail to reject H₀. Show your work.

5. Calculate the critical value(s). Use the test statistic then to make a decision to either reject H₀ or to fail to reject H₀. Show your work.

6. State what your decision means in the context of the problem (prescription expenditure in the Midwest vs. the Northeast). Show your work.

Answer 1

Given:

$1585502645401_blob.png$ = 838, n = 60, $1585502646270_blob.png$ = 745, $1585502645011_blob.png$ = 300, $1585502644998_blob.png$ = 0.05

1)

Hypothesis:

Ho: $1585502645616_blob.png$= 838

Ha: $1585502645038_blob.png$ < 838

One tailed Test (Lower)

2)

$1585502644998_blob.png$ = 0.05

Critical value:

Z$1585502644998_blob.png$ = Z0.05 = -1.645 ........................Using standard Normal table

Decision Rule:

Z < Z$1585502648209_blob.png$ , Then Reject Ho at 5% level of significance.

3)

$\sigma$ is Known, So we can use Z test

Test statistic:

Z-X - 745 – 838 25o = 300/60 = -2.40 300/

4)

P-value = 0.0082 ........................Using standard Normal table

P-value < $\alpha$ , i.e. 0.0082 < 0.05, That is Reject Ho at 5% level of significance.

5)

Critical value:

Z$1585502644998_blob.png$ = Z0.05 = -1.645 ........................Using standard Normal table

Decision Rule:

Z < Z$1585502648209_blob.png$ , Then Reject Ho at 5% level of significance.

6)

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.