2. Can the death rate be influenced by tax incentives? Kopczuk and Slemrod (2003

Question

2. Can the death rate be influenced by tax incentives? Kopczuk and Slemrod (2003) investigated this possibility using data on deaths in the US in years in which the government announced it was changing (usually raising) the tax rate on inheritance (the estate tax). The authors calculated the death rate during the 14 days before, and the 14 days after, the changes in the estate tax took effect. The number of deaths per day in each of these periods is given in the table below. Do the appropriate test to determine whether the death rate changed significantly after the state tax change. Death Rate under Death Rate under Year Higher Estate Tax Rate Lower Estate Tax Rate 1917 22.21 24.93 1918 18.86 20.00 1919 28.21 29.93 1924 31.64 30.64 1926 18.43 20.86 1932 9.50 10.14 1934 24.29 28.00 1935 26.64 25.29 1940 35.07 35.00 1941 38.86 37.57 1942 28.50 34.79 Answers: Ho: Ha: test statistic: df: Exact Prob. of test statistic: Conclusion relative to the hypothesis: *test-statistic refers to the statistical test value for whatever statistical test is done to answer the question. 2. Can the death rate be influenced by tax incentives? Kopczuk and Slemrod (2003) investigated this possibility using data on deaths in the US in years in which the government announced it was changing (usually raising) the tax rate on inheritance (the estate tax). The authors calculated the death rate during the 14 days before, and the 14 days after, the changes in the estate tax took effect. The number of deaths per day in each of these periods is given in the table below. Do the appropriate test to determine whether the death rate changed significantly after the state tax change. Death Rate under Death Rate under Year Higher Estate Tax Rate Lower Estate Tax Rate 1917 22.21 24.93 1918 18.86 20.00 1919 28.21 29.93 1924 31.64 30.64 1926 18.43 20.86 1932 9.50 10.14 1934 24.29 28.00 1935 26.64 25.29 1940 35.07 35.00 1941 38.86 37.57 1942 28.50 34.79 Answers: Ho: Ha: test statistic: df: Exact Prob. of test statistic: Conclusion relative to the hypothesis: *test-statistic refers to the statistical test value for whatever statistical test is done to answer the question.

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.812
since our test is left-tailed
reject Ho, if to < -1.812
we use Test Statistic
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -1.36
We have d = -1.36
pooled variance = calculate value of Sd= S^2 = sqrt [ 75.79-(-14.94^2/11 ] / 10 = 2.36
to = d/ (S/n) = -1.91
critical Value
the value of |t | with n-1 = 10 d.f is 1.812
we got |t o| = 1.91 & |t | =1.812
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -1.9147 ) = 0.04228
hence value of p0.05 > 0.04228,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate,death rate changed significantly after the state tax change H1: Ud < 0
test statistic: -1.91
critical value: reject Ho, if to < -1.812
decision: Reject Ho
p-value: 0.04228

we have evidence that death rate changed significantly after the state tax change

X Y X-Y (X-Y)^2 22.21 24.93 -2.72 7.398 18.86 20 -1.14 1.3 28.21 29.93 -1.72 2.958 31.64 30.64 1 1 18.43 20.86 -2.43 5.905 9.5 10.14 -0.64 0.41 24.29 28 -3.71 13.76 26.64 25.29 1.35 1.823 35.07 35 0.07 0.005 38.86 37.57 1.29 1.664 28.5 34.79 -6.29 39.56 -14.9 75.79

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