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 190 175 177 188 189 179 O Height (cm) of Main Opponent 170 188 180 183 190 177 a. Use the sample data with a 0.05 significance level to test the claim that for the population heights for presidents and their main opponents, the differences have a mean greater than 0 cm. 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. What are the null and alternative hypotheses for the hypothesis test? Họ: Hg = cm H: Ha > (Type integers or decimals. Do not round.) cm Identify the test statistic. t= 0.38 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.361 (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 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 (1) (2). the null hypothesis. (1) O only positive numbers, O zero, O only negative numbers, (2) O fail to reject O reject
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 190 175 177 188 189 179 O Height (cm) of Main Opponent 170 188 180 183 190 177 a. Use the sample data with a 0.05 significance level to test the claim that for the population heights for presidents and their main opponents, the differences have a mean greater than 0 cm. 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. What are the null and alternative hypotheses for the hypothesis test? Họ: Hg = cm H: Ha > (Type integers or decimals. Do not round.) cm Identify the test statistic. t= 0.38 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.361 (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 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 (1) (2). the null hypothesis. (1) O only positive numbers, O zero, O only negative numbers, (2) O fail to reject O reject
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:3. 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
190 175 177 188 189 179 O
Height (cm) of Main Opponent 170 188 180 183 190 177
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, 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. What are the null and alternative hypotheses for the
hypothesis test?
Ho: Ha
cm
H1: Hd
(Type integers or decimals. Do not round.)
cm
Identify the test statistic.
t =
0.38
(Round to two decimal places as needed.)
Identify the P-value.
P-value =
0.361
(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
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 (1)
(2)
the null hypothesis.
(1) O only positive numbers,
(2)
fail to reject
O zero,
O reject
O only negative numbers,
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