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 Height (cm) of Main Opponent 181 189 173 169 189 177 186 182 174 188 193 177 e 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 cm. In this example, Hg is the mean value of the differences d for the population of all pairs of data, where each individual differenced is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test? Họ: Ha = 0 cm H1: Ha > |0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t=- 43 (Round to two decimal places as needed.) Identify the P-value. P-value = 337 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? the significance level, Since the P-value is the null hypothesis. There 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 O cm < Hg < 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 the null hypothesis.
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 Height (cm) of Main Opponent 181 189 173 169 189 177 186 182 174 188 193 177 e 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 cm. In this example, Hg is the mean value of the differences d for the population of all pairs of data, where each individual differenced is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test? Họ: Ha = 0 cm H1: Ha > |0 cm (Type integers or decimals. Do not round.) Identify the test statistic. t=- 43 (Round to two decimal places as needed.) Identify the P-value. P-value = 337 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? the significance level, Since the P-value is the null hypothesis. There 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 O cm < Hg < 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 the null hypothesis.
MATLAB: An Introduction with Applications
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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 | 186 | 182 | 174 | 188 | 193 | 177 |
|--------------------------|-----|-----|-----|-----|-----|-----|
| Height (cm) of Main Opponent | 181 | 189 | 173 | 169 | 189 | 177 |
**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 cm.
In this example, \(\mu_d\) 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?
- \(H_0: \mu_d = 0\) cm
- \(H_1: \mu_d > 0\) cm
(Type integers or decimals. Do not round.)
Identify the test statistic.
- \(t = -0.43\)
(Round to two decimal places as needed.)
Identify the P-value.
- P-value = 0.337
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is [ _greater than_ ] the significance level, [ _fail to reject_ ] the null hypothesis. There [ _is not_ ] 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 \[ -7.8 \ \text{cm} < \mu_d < 4.8 \ \text{cm} \].
(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 [ _0_ ], [ _do not reject_ ] the null hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7f57acd-42b9-466e-a85d-4609f38f005a%2Facbac3de-2ad3-415c-94d2-943369e6270c%2Fouar6ho_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 | 186 | 182 | 174 | 188 | 193 | 177 |
|--------------------------|-----|-----|-----|-----|-----|-----|
| Height (cm) of Main Opponent | 181 | 189 | 173 | 169 | 189 | 177 |
**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 cm.
In this example, \(\mu_d\) 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?
- \(H_0: \mu_d = 0\) cm
- \(H_1: \mu_d > 0\) cm
(Type integers or decimals. Do not round.)
Identify the test statistic.
- \(t = -0.43\)
(Round to two decimal places as needed.)
Identify the P-value.
- P-value = 0.337
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is [ _greater than_ ] the significance level, [ _fail to reject_ ] the null hypothesis. There [ _is not_ ] 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 \[ -7.8 \ \text{cm} < \mu_d < 4.8 \ \text{cm} \].
(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 [ _0_ ], [ _do not reject_ ] the null hypothesis.
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