Answered: The z-statistic for this hypothesis…

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 study was performed to investigate whether teens and adults had different habits when it comes to consuming meat-free meals. In particular, the researchers were interested in the relationship between p₁, the proportion of teens who would report eating at least one meat-free meal in the past week, and p₂, the proportion of adults who would report eating at least one meat-free meal in the past week. A random sample of 875 teens and a separate random sample of 2,323 adults found that 555 of the teens and 1,601 of the adults reported eating at least one meat-free meal in the past week. The conditions for inference were checked and verified.

The z-statistic for this hypothesis test was z = –2.95. Based on this z-statistic, what is the P-value and what is the conclusion the researchers should reach for this test?

A. The P-value = 0.0016 and, because this P-value is very small, the conclusion should be that teens and adults differ in the proportion of their meat-free meals.

B. The P-value = 0.0031 and, because this P-value is very small, the conclusion should be that teens and adults differ in the proportion of their meat-free meals.

C. The P-value = 0.0016 and, because this P-value is large, there is not enough evidence to conclude that there is a significant difference in the proportions of the meat-free meals that are eaten by teens and adults.

D. The P-value = 0.0031 and, because this P-value is large, there is not enough evidence to conclude that there is a significant difference in the proportions of the meat-free meals that are eaten by teens and adults.

E. The P-value = 0.9969 and, because this P-value is large, there is not enough evidence to conclude that there is a significant difference in the proportions of the meat-free meals that are eaten by teens and adults.

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