The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed in the accompanying table are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Complete parts (a) through (c). - September April 68 71 57 81 68 56 65 64 71 64 69 58 82 69 58 68 68 77 a. Use a 0.05 significance level to test the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. In this example, Hd 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 April weight minus the September weight. What are the null and alternative hypotheses for the hypothesis test? Ho Hd 0 kg H₁ Hd > 0 kg (Type integers or decimals. Do not round.) Identify the test statistic. t= 1.33 (Round to two decimal places as needed.). Identify the P-value. P-value = 0.113 (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, do not reject the null hypothesis. There is not sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. 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 kg
The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed in the accompanying table are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Complete parts (a) through (c). - September April 68 71 57 81 68 56 65 64 71 64 69 58 82 69 58 68 68 77 a. Use a 0.05 significance level to test the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. In this example, Hd 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 April weight minus the September weight. What are the null and alternative hypotheses for the hypothesis test? Ho Hd 0 kg H₁ Hd > 0 kg (Type integers or decimals. Do not round.) Identify the test statistic. t= 1.33 (Round to two decimal places as needed.). Identify the P-value. P-value = 0.113 (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, do not reject the null hypothesis. There is not sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. 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 kg
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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Transcribed Image Text:The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their
freshman year. Listed in the accompanying table are weights (kg) of randomly selected male
college freshmen. The weights were measured in September and later in April. Use the listed
paired sample data, and assume that the samples are simple random samples and that the
differences have a distribution that is approximately normal. Complete parts (a) through (c).
-
September
April
68 71 57 81 68 56 65 64 71
64 69 58 82 69 58 68 68 77
a. Use a 0.05 significance level to test the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April.
In this example, Hd 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 April weight minus the September weight. What
are the null and alternative hypotheses for the hypothesis test?
Ho Hd
0 kg
H₁ Hd > 0 kg
(Type integers or decimals. Do not round.)
Identify the test statistic.
t= 1.33 (Round to two decimal places as needed.).
Identify the P-value.
P-value = 0.113 (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, do not reject the null hypothesis. There is not sufficient evidence to support the claim that for the population of freshman male
college students, the weights in September are less than the weights in the following April.
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 kg <H<kg.
(Type integers or decimals rounded to one decimal place as needed.)
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