Question 1 Can the death rate be influenced by tax incentives? Kopczuk and Selmrod (2003) investigated this possibility
Posted: Tue Jul 05, 2022 9:55 am
Question 1
Can the death rate be influenced by tax incentives?Kopczuk and Selmrod (2003) investigated this possibility using dataon deaths in the U.S. in years in which the government announced itwas raising the tax rate on inheritance. The authors calculate thedeath rate during the 14 days before and the 14 days after, thechanges in the tax rates took effect. The data is shown in thetable.
Year
Death rate under higher estate tax rate
Death rate under lower estate tax rate
Difference in estate tax rate (high - low )
1917
22.21
24.93
2.72
1918
18.86
20.00
1.14
1919
28.21
29.93
1.72
1924
31.64
30.64
1
1926
18.43
20.86
2.43
1932
9.5
10.14
0.64
1934
24.29
28.00
3.71
1935
26.64
25.29
1.35
1940
35.07
35.00
0.07
1041
38.86
37.57
1.29
1942
28.5
34.79
6.29
What kind of t-test is appropriate for this study,one-sample t-test, paired t-test or two-sample t-test?Why?
Write the null and alternative hypothesis for thet-test.
Use R to conduct the t-test and determine the p-value.Paste a R screenshot below
Interpret the p-value and state the conclusion from yourtest
Question 2.
The male of stalk-eyed flies has long eye stalks. Thefemales use the length go the eye stalks to choose mates. Is themale’s eye stalk length affected by its diet? An experiment wasconducted to test this question. In the experiment, two groups ofmale stalk-eyed flies were fed on two different diets. One groupwas fed on corn, and the other was fed on cotton wool. The eyestalk length was recorded in millimeters for different number ofindividuals from the two groups. The raw data are shownbelow:
Corn diet: 2.15, 2.14, 2.13, 2.13, 2.12, 2.11, 2.10,2.08, 2.08, 2.08, 2.04, 2.05, 2.03, 2.02, 2.01, 2.00, 1.99, 1.96,1.95, 1.93, 1.89
Cotton diet: 2.12, 2.07, 2.01, 1.93, 1.77, 1.68, 1.64,1.61, 1.59, 1.58, 1.56, 1.55, 1.54, 1.49, 1.45, 1.43, 1.39, 1.34,1.33, 1.29, 1.26, 1.24, 1.11, 1.05
What kind of t-test is appropriate for this study,one-sample t-test, paired t-test or two-sample t-test?Why?
Write the null and alternative hypothesis for thet-test.
Calculate the mean, variance and sample size for eachgroup.
Mean
Variance
Sample size
Corn diet
Cotton diet
Use R to conduct the t-test. Paste a R screenshotbelow.
What is the p-value? Can the null hypothesis berejected?
Based on the t-test, determine whether the diet affectthe eye stalk length.
Question 3
As our planet warms, the change in temperature will havemajor effects on life. One of the possibilities for what mighthappen to a species is that species can move closer to the poles sothat it experienced temperatures closer to what it has experiencedin the past. A recent study of the range of limits of Europeanbutterflies found that, of 24 species that had changed their rangesin the last 100 years, 22 of them had moved further north and onlytwo had moved further south. Assume that these 24 species are arandom sample of butterfly species. Conduct a binomial test to testthe hypothesis that the fraction of butterfly species moving northis different from the fraction movingsouth.
Write the null and alternative hypothesis for thebinomial test. (hint: null hypothesis is that the chance of speciesmoving north or south is the same)
What is the observed value for this binomialtest?
List all possible outcomes in which the number ofbutterfly species moving north is greater than the 22observed.
Use R to conduct the binomial test and determine thep-value. Paste a R screenshot below.
Interpret the p-value and state the conclusion from yourtest
Can the death rate be influenced by tax incentives?Kopczuk and Selmrod (2003) investigated this possibility using dataon deaths in the U.S. in years in which the government announced itwas raising the tax rate on inheritance. The authors calculate thedeath rate during the 14 days before and the 14 days after, thechanges in the tax rates took effect. The data is shown in thetable.
Year
Death rate under higher estate tax rate
Death rate under lower estate tax rate
Difference in estate tax rate (high - low )
1917
22.21
24.93
2.72
1918
18.86
20.00
1.14
1919
28.21
29.93
1.72
1924
31.64
30.64
1
1926
18.43
20.86
2.43
1932
9.5
10.14
0.64
1934
24.29
28.00
3.71
1935
26.64
25.29
1.35
1940
35.07
35.00
0.07
1041
38.86
37.57
1.29
1942
28.5
34.79
6.29
What kind of t-test is appropriate for this study,one-sample t-test, paired t-test or two-sample t-test?Why?
Write the null and alternative hypothesis for thet-test.
Use R to conduct the t-test and determine the p-value.Paste a R screenshot below
Interpret the p-value and state the conclusion from yourtest
Question 2.
The male of stalk-eyed flies has long eye stalks. Thefemales use the length go the eye stalks to choose mates. Is themale’s eye stalk length affected by its diet? An experiment wasconducted to test this question. In the experiment, two groups ofmale stalk-eyed flies were fed on two different diets. One groupwas fed on corn, and the other was fed on cotton wool. The eyestalk length was recorded in millimeters for different number ofindividuals from the two groups. The raw data are shownbelow:
Corn diet: 2.15, 2.14, 2.13, 2.13, 2.12, 2.11, 2.10,2.08, 2.08, 2.08, 2.04, 2.05, 2.03, 2.02, 2.01, 2.00, 1.99, 1.96,1.95, 1.93, 1.89
Cotton diet: 2.12, 2.07, 2.01, 1.93, 1.77, 1.68, 1.64,1.61, 1.59, 1.58, 1.56, 1.55, 1.54, 1.49, 1.45, 1.43, 1.39, 1.34,1.33, 1.29, 1.26, 1.24, 1.11, 1.05
What kind of t-test is appropriate for this study,one-sample t-test, paired t-test or two-sample t-test?Why?
Write the null and alternative hypothesis for thet-test.
Calculate the mean, variance and sample size for eachgroup.
Mean
Variance
Sample size
Corn diet
Cotton diet
Use R to conduct the t-test. Paste a R screenshotbelow.
What is the p-value? Can the null hypothesis berejected?
Based on the t-test, determine whether the diet affectthe eye stalk length.
Question 3
As our planet warms, the change in temperature will havemajor effects on life. One of the possibilities for what mighthappen to a species is that species can move closer to the poles sothat it experienced temperatures closer to what it has experiencedin the past. A recent study of the range of limits of Europeanbutterflies found that, of 24 species that had changed their rangesin the last 100 years, 22 of them had moved further north and onlytwo had moved further south. Assume that these 24 species are arandom sample of butterfly species. Conduct a binomial test to testthe hypothesis that the fraction of butterfly species moving northis different from the fraction movingsouth.
Write the null and alternative hypothesis for thebinomial test. (hint: null hypothesis is that the chance of speciesmoving north or south is the same)
What is the observed value for this binomialtest?
List all possible outcomes in which the number ofbutterfly species moving north is greater than the 22observed.
Use R to conduct the binomial test and determine thep-value. Paste a R screenshot below.
Interpret the p-value and state the conclusion from yourtest