Question

Use the following data on number of deaths from drug overdose for sample of different states. We separated states to two groups based on whether a certain drug law is being enacted or not. The states where the law is enacted are called BLUE states and those not using this law are called RED states. (Note that there are 8 observations in each group)

Table: Number of overdose deaths every year in different states.

(BLUE States) - enacting the new drug law	(RED States) - NOT enacting the new drug law
43	29
25	72
64	49
17	86
36	78
21	45
53	38
19	45

What is the t-statistics for testing the hypothesis that the average deaths in BLUE states is equal to 30 per year.

1.96

5.67

0.77

0.27

Same question for RED states:

2. What is the t-statistics for testing the hypothesis that the average deaths in RED states is equal to 30 per year.

7.57

1.22

2.36

3.46

3. What is the p-value for the two-sided test about average deaths in BLUE states being equal 30? (Use T-distribution)

0.23

0.11

0.92

0.46

4. Same question for RED states:

What is the p-value for the two-sided test about average deaths in RED states being equal 30? (Use T-distribution)

0.03

0.14

0.08

0.01

5. Given the t-stats (or p-values) that you have obtained so far for both BLUE and RED states, what can you tell about the two-sided hypothesis of 30 average deaths in either states at 5% significance level?

Fail to reject for both

Reject for both

Reject for BLUE ; Fail to reject for RED

Fail to reject for BLUE ; Reject for RED

6. Now we are interested to check the effectiveness of the new drug law:

or similarly

What is the standard error of the differences in the means? (Assume Large Sample Properties, i.e. Normal Distribution)

5.14

9.53

10.19

6.71

7. Same as previous question: We are interested to check the effectiveness of the new drug law:

H 0 ; L a w i s N O T e f f e c t i v e v s . H 1 ; L a w i s e f f e c t i v e

or similarly

H 0 ; E ( B L U E ) − E ( R E D ) = 0 v s . H 1 ; E ( B L U E ) − E ( R E D ) < 0

What is the t-statistics for this hypothesis test?

-2.15

-0.27

-1.91

-1.23

Same as previous question: We are interested to check the effectiveness of the new drug law:

H 0 ; L a w i s N O T e f f e c t i v e v s . H 1 ; L a w i s e f f e c t i v e

or similarly

H 0 ; E ( B L U E ) − E ( R E D ) = 0 v s . H 1 ; E ( B L U E ) − E ( R E D ) < 0

8. Which of the following is correct given your answers to question 7 ? (Note: one-sided test. Also use Normal Distribution)(Hint: find p-value)

None of the given choices are correct

We reject H0 at 1% significance level

We FAIL to reject H0 at 5% significance level

We reject H0 at 10% significance level

Answer 1

Blue States	Red states
43	29
25	72
64	49
17	86
36	78
21	45
53	38
19	45
278=sum	442=sum
34.75=	55.25=
17.343=sd	20.631=sd

1)

The t-statistics for testing the hypothesis that the average deaths in BLUE states is equal to 30 per year.

t = 0.77

2)

The t-statistics for testing the hypothesis that the average deaths in RED states is equal to 30 per year.

t = 3.46

3)

The p-value for the two-sided test about average deaths in BLUE states being equal 30

= 0.46

4)

the p-value for the two-sided test about average deaths in RED states being equal 30

= 0.01

5)

Given the t-stats (or p-values) that we have obtained so far for both BLUE and RED states,

Fail to reject for BLUE ; Reject for RED.

6)

The standard error of the differences in the means is

= 9.53

7)

the t-statistics for this hypothesis test for the difference,

  

= -2.15

8)

P-value = 0.025 < 0.05, 0.10 but > 0.01

We reject H0 at 10% significance level.

****If you haveany queries or doubts please comment below, if you're satisfied please give a like. Thank you!