A popular heory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. Height (cm) of President 176 171 184 174 184 165 Height (om) of Main Opponent 104 181 106 173 182 178 a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main opponents. the differences have a mean greater than 0 em. In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. WWhat are the null and alternative hypotheses for the hypothesis test? Ho: H cm H: om (Type integers or decimals. Do not round.) Identify the test statistio. -(Round to two decimal places as needed.) Identify the P.value. P.value (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is V the significance level Vthe null hypothesis. There V suficient evidence to support the elaim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is om
A popular heory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. Height (cm) of President 176 171 184 174 184 165 Height (om) of Main Opponent 104 181 106 173 182 178 a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main opponents. the differences have a mean greater than 0 em. In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. WWhat are the null and alternative hypotheses for the hypothesis test? Ho: H cm H: om (Type integers or decimals. Do not round.) Identify the test statistio. -(Round to two decimal places as needed.) Identify the P.value. P.value (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is V the significance level Vthe null hypothesis. There V suficient evidence to support the elaim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is om
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below.
Height (cm) of President
176 171 184 174
184 165 D
Height (cm) of Main Opponent 184 181 188 173 182 178
a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than O cm.
In this example, Pd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test?
Ho: Ha cm
H1: Ha
(Type integers or decimals. Do not round.)
cm
Identify the test statistic.
t= (Round to two decimal places as needed.)
Identify the P-value.
P-value = (Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is
V the significance level,
the null hypothesis. There
V sufficient evidence to support the claim that presidents tend to be taller than their opponents.
b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is cm <Ha
cm.
(Round to one decimal place as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
Since the confidence interval contains
V the null hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedef5f47-f6d8-44fa-bbe6-df7f419d88eb%2F10c0d2f8-f94f-4d2f-9258-400fbe928740%2F66fu9p9_processed.png&w=3840&q=75)
Transcribed Image Text:A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below.
Height (cm) of President
176 171 184 174
184 165 D
Height (cm) of Main Opponent 184 181 188 173 182 178
a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than O cm.
In this example, Pd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test?
Ho: Ha cm
H1: Ha
(Type integers or decimals. Do not round.)
cm
Identify the test statistic.
t= (Round to two decimal places as needed.)
Identify the P-value.
P-value = (Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is
V the significance level,
the null hypothesis. There
V sufficient evidence to support the claim that presidents tend to be taller than their opponents.
b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is cm <Ha
cm.
(Round to one decimal place as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
Since the confidence interval contains
V the null hypothesis.
![A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from nomally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.
ProctoredNonproctored
P1
H2
n
32
35
77.98
86.03
11.43
18.15
a. Use a 0.05 significance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests
What are the null and alternative hypotheses?
O A. Ho: H1 #H2
H: H <P2
OB. Ho: H1= H2
H: H H2
OC. Ho: H1 =H2
OD. Ho: H1= H2
H: <P2
H: H1 > H2
The test statistic, t, is |- (Round to two decimal places as needed.)
The P-value is . (Round to three decimal places as needed.)
State the conclusion for the test.
O A. Reject Ho. There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O B. Fail to reject Hn. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O C. Fail to reject Ho- There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O D. Reject Ho. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
b. Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
(Round to two decimal places as needed.)
Does the confidence interval support the conclusion of the test?
V because the confidence interval contains](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedef5f47-f6d8-44fa-bbe6-df7f419d88eb%2F10c0d2f8-f94f-4d2f-9258-400fbe928740%2F18yv_processed.png&w=3840&q=75)
Transcribed Image Text:A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from nomally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.
ProctoredNonproctored
P1
H2
n
32
35
77.98
86.03
11.43
18.15
a. Use a 0.05 significance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests
What are the null and alternative hypotheses?
O A. Ho: H1 #H2
H: H <P2
OB. Ho: H1= H2
H: H H2
OC. Ho: H1 =H2
OD. Ho: H1= H2
H: <P2
H: H1 > H2
The test statistic, t, is |- (Round to two decimal places as needed.)
The P-value is . (Round to three decimal places as needed.)
State the conclusion for the test.
O A. Reject Ho. There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O B. Fail to reject Hn. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O C. Fail to reject Ho- There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
O D. Reject Ho. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
b. Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
(Round to two decimal places as needed.)
Does the confidence interval support the conclusion of the test?
V because the confidence interval contains
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