A physical education professor believes that exercise can slow the aging process

Question

A physical education professor believes that exercise can slow the aging process. For the past 10 years, he has been conducting an exercise class for 14 individuals who are currently 50 years old. Normally, as one ages, maximum oxygen consumption decreases. The national norm for maximum oxygen consumption in 50-year-old individuals is 30 milliliters per kilogram per minute, with a standard deviation of 9.5. The mean of the 14 individuals is 36 milliliters per kilogram per minute. What do you conclude? Use = 0.051 tail.

zobt =

zcrit =

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 30 (No effect on ageing process)

Alternative hypothesis: > 30 (Exercise can slow aging process)

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.051. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE),z statistic test statistic (z).

SE = s / sqrt(n),

S.E = 2.539

z = (x - ) / SE

z = 2.36314

z critical = + 1.951

Rejection region is:-

z > 1.951

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Interpret results. Since the z-value (2.36) lies in rejection region so we have to reject the null hypothesis.

From this we can conclude that we have sufficient evidence in the favor of the claim that exercise can slow the aging process.

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