For PPObléms 38. to 43., consider the following: A political scientist is interested in evaluating the impact the COVID-19 pandemic had on the 2020 pre As a part of her study, she has sampled election day per capita COVID-19 incidence and death rates (7 won by each candidate. The information she has collected appear in the table below: State Won by 1 3 4 8. Biden WI Incidence Rate 4.290% NV WA IL MN VA GA CT 3.281% 1.411% 3.446% 2.756% 2.154% 3.668% 2.101% Death Rate 0.037% 0.058% 0.031% 0.080% 0.045% 0.043% 0.075% 0.130% Trump Indidence Rate 2.578% WY NC SC MT мо UT OK AL 2.642% 3.454% 3.235% 3.087% 3.637% 3.362% 3.992% Death Rate 0.016% 0.042% 0.076% 0.037% 0.050% 0.019% 0.035% 0.061%
For PPObléms 38. to 43., consider the following: A political scientist is interested in evaluating the impact the COVID-19 pandemic had on the 2020 pre As a part of her study, she has sampled election day per capita COVID-19 incidence and death rates (7 won by each candidate. The information she has collected appear in the table below: State Won by 1 3 4 8. Biden WI Incidence Rate 4.290% NV WA IL MN VA GA CT 3.281% 1.411% 3.446% 2.756% 2.154% 3.668% 2.101% Death Rate 0.037% 0.058% 0.031% 0.080% 0.045% 0.043% 0.075% 0.130% Trump Indidence Rate 2.578% WY NC SC MT мо UT OK AL 2.642% 3.454% 3.235% 3.087% 3.637% 3.362% 3.992% Death Rate 0.016% 0.042% 0.076% 0.037% 0.050% 0.019% 0.035% 0.061%
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![A political scientist is interested in evaluating the impact the COVID-19 pandemic had on the 2020 presidential election.
For Problems 38. to 43., consider the following:
As a part of her study, she has sampled election day per capita COVID-19 incidence and death rates (%) for 10 states
won by each candidate. The information she has collected appear in the table below:
State Won by
2
4
8.
9.
10
Biden
Incidence Rate 4.290%
WI
NV
WA
IL
MN
VA
GA
CT
NM
MD
3.281%
1.411%
3.446%
2.756%
2.154%
3.668%
2.101%
2.349%
2.446%
Death Rate
0.037%
0.058%
0.031%
0.080%
0.045%
0.043%
0.075%
0.130%
0.050%
0.069%
Trump
Indidence Rate 2.578%
WY
NC
SC
MT
MO
UT
OK
AL
SD
TX
2.642%
3.454%
3.235%
3.087%
3.637%
3.362%
3.992%
5.410%
3.111%
Death Rate
0.016%
0.042%
0.076%
0.037%
0.050%
0.019%
0.035%
0.061%
0.049%
0.062%
These results show no significant deviation from being normally distributed.
38. Given that the sample average incidence rate for the states won by Biden, ig = 2.79%, is less than the SC sample mean
incidence rate for the states won by Trump, ir = 3.45%, the desire is to determine if this data suggests that the mean
incidence rate for states won by Biden is less than that for the states carried by Trump. What would suitable research (H1)
and null (Ho) hypotheses be:
a. Hi: īg – Xp < 0
Họ: XB – XT 2 0
b. H1 HB - HT < 0
Họ: HB - HT = 0
erl navia
c. H1: HB > HT
Họ: HB = HT
d. H1: Xg - xr < 0.66%
Họ: xg - X = 0.66%
39. Given that the respective sample standard deviations are sR = 0.87% and sT = 0.81%, what test statistic would be
both appropriate to use and provide potentially the most powerful test of the hypothesis selected above?
d-0.66
t =
Sa/V10
where d =
E1 di , with di = xB - XT, for i = 1,.10 and så = ¿E}º,(d; - d)²
a.
od et ollo no
where of and of are the respective population variances
b. Z =
tol
ollot sd to
10 ' 10
where spooled =
S+ s7
C.
t =
Spooled 10* 10
Wasemioga
d.
t' =
V10' 10
ain has four
40. The null distribution of the test statistic selected above is:
a. Student-t with d.f. = 9
b. Standard Normal c. Student-t with d.f. = 20
d. Student-t with d.f. = 18
41. Suppose we decide to perform the test at a = 0.01 level of significance. What is the decision rule to be applied to
the test statistic identified in Problem 39. above for this test?
a. Reject Ho if the Test Statistic is < -2.821 = t(9, 0.01)
b. Reject Ho if the Test Statistic is < -2.326 = Z(0.01)
slomst
c. Reject Ho if the Test Statistic is < -2.552 = t(18, 0.01)
d. Reject Ho if the Test Statistic is < -2.528 = t(20,0.01)
42. If the test statistic is equal to -3.94. The observed significance level (p-value) is:
a. P[ t9) < -3.94] = 0.00171
b. P[ Z < -3.94] = 0.00004
aoni
Noo namow n
nsa ords Boni2 d
c. P[ t(18) < -3.94] = 0.00048
d. P[t/20) <-3.94] = 0.00041
43. Based on a = 0.01, and the p-value above, the decision and conclusion for the hypothesis test are: t
ow
a. reject Ho; conclude mean incidence rate lower in states won by Trump
b. fail to reject Ho; conclude mean incidence rate is
c. reject Ho; conclude mean incidence rate higher in states won by Trump
d. fail to reject Ho; conclude insufficient evidence to identify an incidence rate difference across states won by
esame regardless of who won the state
the two candidates](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9db3453-6b51-40e6-9d62-12c75a54c2dd%2F79c62097-6fd0-4aea-aa7a-c857d37983d0%2Fvfnrqr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A political scientist is interested in evaluating the impact the COVID-19 pandemic had on the 2020 presidential election.
For Problems 38. to 43., consider the following:
As a part of her study, she has sampled election day per capita COVID-19 incidence and death rates (%) for 10 states
won by each candidate. The information she has collected appear in the table below:
State Won by
2
4
8.
9.
10
Biden
Incidence Rate 4.290%
WI
NV
WA
IL
MN
VA
GA
CT
NM
MD
3.281%
1.411%
3.446%
2.756%
2.154%
3.668%
2.101%
2.349%
2.446%
Death Rate
0.037%
0.058%
0.031%
0.080%
0.045%
0.043%
0.075%
0.130%
0.050%
0.069%
Trump
Indidence Rate 2.578%
WY
NC
SC
MT
MO
UT
OK
AL
SD
TX
2.642%
3.454%
3.235%
3.087%
3.637%
3.362%
3.992%
5.410%
3.111%
Death Rate
0.016%
0.042%
0.076%
0.037%
0.050%
0.019%
0.035%
0.061%
0.049%
0.062%
These results show no significant deviation from being normally distributed.
38. Given that the sample average incidence rate for the states won by Biden, ig = 2.79%, is less than the SC sample mean
incidence rate for the states won by Trump, ir = 3.45%, the desire is to determine if this data suggests that the mean
incidence rate for states won by Biden is less than that for the states carried by Trump. What would suitable research (H1)
and null (Ho) hypotheses be:
a. Hi: īg – Xp < 0
Họ: XB – XT 2 0
b. H1 HB - HT < 0
Họ: HB - HT = 0
erl navia
c. H1: HB > HT
Họ: HB = HT
d. H1: Xg - xr < 0.66%
Họ: xg - X = 0.66%
39. Given that the respective sample standard deviations are sR = 0.87% and sT = 0.81%, what test statistic would be
both appropriate to use and provide potentially the most powerful test of the hypothesis selected above?
d-0.66
t =
Sa/V10
where d =
E1 di , with di = xB - XT, for i = 1,.10 and så = ¿E}º,(d; - d)²
a.
od et ollo no
where of and of are the respective population variances
b. Z =
tol
ollot sd to
10 ' 10
where spooled =
S+ s7
C.
t =
Spooled 10* 10
Wasemioga
d.
t' =
V10' 10
ain has four
40. The null distribution of the test statistic selected above is:
a. Student-t with d.f. = 9
b. Standard Normal c. Student-t with d.f. = 20
d. Student-t with d.f. = 18
41. Suppose we decide to perform the test at a = 0.01 level of significance. What is the decision rule to be applied to
the test statistic identified in Problem 39. above for this test?
a. Reject Ho if the Test Statistic is < -2.821 = t(9, 0.01)
b. Reject Ho if the Test Statistic is < -2.326 = Z(0.01)
slomst
c. Reject Ho if the Test Statistic is < -2.552 = t(18, 0.01)
d. Reject Ho if the Test Statistic is < -2.528 = t(20,0.01)
42. If the test statistic is equal to -3.94. The observed significance level (p-value) is:
a. P[ t9) < -3.94] = 0.00171
b. P[ Z < -3.94] = 0.00004
aoni
Noo namow n
nsa ords Boni2 d
c. P[ t(18) < -3.94] = 0.00048
d. P[t/20) <-3.94] = 0.00041
43. Based on a = 0.01, and the p-value above, the decision and conclusion for the hypothesis test are: t
ow
a. reject Ho; conclude mean incidence rate lower in states won by Trump
b. fail to reject Ho; conclude mean incidence rate is
c. reject Ho; conclude mean incidence rate higher in states won by Trump
d. fail to reject Ho; conclude insufficient evidence to identify an incidence rate difference across states won by
esame regardless of who won the state
the two candidates
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