A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years. Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners? (A) z=\frac{84.2-79.2}{\sqrt{5(100-5)\left ( \frac{1}{50}+\frac{1}{50} \right ))}}z=5(100−5)(501+501))84.2−79.2 (B) z=\frac{84.2-79.2}{\frac{3.4}{\sqrt{80}}}z=803.484.2−79.2 (C) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}+\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2 (D) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}}+\sqrt{\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2 (E) t=\frac{84.2-79.2}{\frac{10.2}{\sqrt{50}}-\frac{6.8}{\sqrt{30}}}t=5010.2−306.884.2−79.2
A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years. Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners? (A) z=\frac{84.2-79.2}{\sqrt{5(100-5)\left ( \frac{1}{50}+\frac{1}{50} \right ))}}z=5(100−5)(501+501))84.2−79.2 (B) z=\frac{84.2-79.2}{\frac{3.4}{\sqrt{80}}}z=803.484.2−79.2 (C) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}+\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2 (D) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}}+\sqrt{\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2 (E) t=\frac{84.2-79.2}{\frac{10.2}{\sqrt{50}}-\frac{6.8}{\sqrt{30}}}t=5010.2−306.884.2−79.2
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years.
Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?
- (A) z=\frac{84.2-79.2}{\sqrt{5(100-5)\left ( \frac{1}{50}+\frac{1}{50} \right ))}}z=5(100−5)(501+501))84.2−79.2
- (B) z=\frac{84.2-79.2}{\frac{3.4}{\sqrt{80}}}z=803.484.2−79.2
- (C) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}+\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2
- (D) t=\frac{84.2-79.2}{\sqrt{\frac{10.2^2}{50}}+\sqrt{\frac{6.8^2}{30}}}t=5010.22+306.8284.2−79.2
- (E) t=\frac{84.2-79.2}{\frac{10.2}{\sqrt{50}}-\frac{6.8}{\sqrt{30}}}t=5010.2−306.884.2−79.2
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