How would you like to live to be 200 years old? For

Chapter 10, Problem 53E

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QUESTION:

How would you like to live to be 200 years old? For centuries, humankind has sought the key to the mystery of aging. What causes aging? How can aging be slowed? Studies have focused on biomarkers, physical or biological changes that occur at a predictable time in a person's life. The theory is that, if ways can be found to delay the occurrence of these biomarkers, human life can be extended. A key biomarker, according to scientists, is forced vital capacity (FVC), the volume of air that a person can expel after taking a deep breath. A study of 5209 men and women aged 30 to 62 showed that FVC declined, on the average,  deciliters (dl) per decade for men and  deciliters per decade for women. \(10) Suppose that you wished to determine whether a physical fitness program for men and women aged 50 to 60 would delay aging; to do so, you measured the FVC for 30 men and 30 women participating in the fitness program at the beginning and end of the 50 - to 60 -year age interval and recorded the drop in FVC for each person. A summary of the data appears in the accompanying table.

Men

Women

Sample size

30

30

Sample average drop in FVC (dI)

Sample standard deviation (dl)

Population mean drop in FVC

\(\mu_{1}\)

\(\mu_{2}\)

Equation transcription:

Text transcription:

10

\mu{1}

\mu{2}

Questions & Answers

QUESTION:

How would you like to live to be 200 years old? For centuries, humankind has sought the key to the mystery of aging. What causes aging? How can aging be slowed? Studies have focused on biomarkers, physical or biological changes that occur at a predictable time in a person's life. The theory is that, if ways can be found to delay the occurrence of these biomarkers, human life can be extended. A key biomarker, according to scientists, is forced vital capacity (FVC), the volume of air that a person can expel after taking a deep breath. A study of 5209 men and women aged 30 to 62 showed that FVC declined, on the average,  deciliters (dl) per decade for men and  deciliters per decade for women. \(10) Suppose that you wished to determine whether a physical fitness program for men and women aged 50 to 60 would delay aging; to do so, you measured the FVC for 30 men and 30 women participating in the fitness program at the beginning and end of the 50 - to 60 -year age interval and recorded the drop in FVC for each person. A summary of the data appears in the accompanying table.

Men

Women

Sample size

30

30

Sample average drop in FVC (dI)

Sample standard deviation (dl)

Population mean drop in FVC

\(\mu_{1}\)

\(\mu_{2}\)

Equation transcription:

Text transcription:

10

\mu{1}

\mu{2}

ANSWER:

Step 1 of 4

The given sample information as;

(a) The null hypothesis and alternative hypothesis define as;

Null hypothesis, s

Alternative hypothesis,

From the given data;

Sample size

Mean

Standard deviation

Then, the test statistic follows as;

From the  value table;

Therefore, the significance level is .

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