A study was to be undertaken to determine if a particular training program would improve physical fitness.An SRS of 31 university students was selected to be enrolled in the fitness program.One important measure of fitness is maximum oxygen uptake.Measurements of oxygen uptake in untrained individuals are known to follow a Normal distribution with a mean of $\mu$ = 45 mL/kg/min.The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects.The measurements made on the subjects coming into this study produced a mean of = 47.4 mL/kg/min with a standard deviation of s = 5.3mL/kg/min.If the 98% confidence interval were determined to be (45.2,49.6)an interval,which may or may not be correct,what would the researchers conclude?
A)The sample is not statistically significant at the 0.02 level.
B)The sample mean is significantly different from $\mu$ = 45 at the 0.04 level.
C)There would be no reason to believe the selected students come from a different population.
D)At the 0.02 level of significance,there is evidence to conclude that the sample comes from a population with a mean different from $\mu$= 45.
E)The true mean oxygen uptake for these students is $\mu$ = 45.

Question

A study was to be undertaken to determine if a particular training program would improve physical fitness.An SRS of 31 university students was selected to be enrolled in the fitness program.One important measure of fitness is maximum oxygen uptake.Measurements of oxygen uptake in untrained individuals are known to follow a Normal distribution with a mean of $\mu$ = 45 mL/kg/min.The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects.The measurements made on the subjects coming into this study produced a mean of  = 47.4 mL/kg/min with a standard deviation of s = 5.3mL/kg/min.If the 98% confidence interval were determined to be (45.2,49.6)an interval,which may or may not be correct,what would the researchers conclude?
A)The sample is not statistically significant at the 0.02 level. 
B)The sample mean is significantly different from $\mu$ = 45 at the 0.04 level. 
C)There would be no reason to believe the selected students come from a different population. 
D)At the 0.02 level of significance,there is evidence to conclude that the sample comes from a population with a mean different from $\mu$= 45. 
E)The true mean oxygen uptake for these students is $\mu$ = 45.

Quizplus · Accepted Answer

The 98% confidence interval is (45.2,49.6), which means we are 98% confident that the true population mean falls within this range. Since the interval does not include the population mean of 45, we can conclude that there is evidence to suggest that the sample comes from a population with a mean that is different from 45. This conclusion is supported by choice D. Option A is incorrect because the sample is statistically significant at the 0.02 level based on the confidence interval. Option B is incorrect because it states that the sample mean is significantly different from the population mean at the 0.04 level, which is not based on any statistical evidence. Option C is incorrect because there is evidence to suggest that the selected students come from a different population based on the confidence interval. Option E is incorrect because the true mean oxygen uptake for the students is unknown and could be anywhere within the confidence interval.

A Study Was to Be Undertaken to Determine If a Particular