Question

Researchers at Texas A&M studied the effect of using standing height desks in an elementary school on the energy expended by nine students. In their paper about the study, they reported descriptive statistics for the nine students. These descriptive statistics were expressed as a mean plus or minus a standard deviation. One such descriptive statistic was the weight of students before using the standing desks, which was reported as 27.0 ± 7.9 kilograms. (This exercise is also a warning to read carefully: that 27.0 ± 7.9 is not a confidence interval, yet summaries in this form are common in scientific reports.) What is ¯ x for these students? (Round your answer to a whole number).

Answer 1

Answer:

For this case we know that "the descriptive statistics were expressed as a mean plus or minus a standard deviation."

And the report is $27 \pm 7.9$

So then we can conclude that $\bar X = 27.0$ and $s =7.9$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)  

s represent the sample standard deviation  

n=9 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:  

$\bar X \pm z_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)  

For this case we know that "the descriptive statistics were expressed as a mean plus or minus a standard deviation."

And the report is $27 \pm 7.9$

So then we can conclude that $\bar X = 27.0$ and $s =7.9$

Answer 2

The value of sample mean $\bar{X}$ for the given number of students is 27.

Given data:

The weight of students before using the standing desks is, (27.0 ± 7.9) kilograms.

The given problem is based on following concepts:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The expression for the confidence interval is,

$\bar{X} \pm s$

Here, $\bar{X}$ is the sample mean for the sample. And s is the Standard deviation.

Comparing the given equation we get,

$\bar{X} = 27\\s = 7.9$

Thus, we can conclude that the value of sample mean $\bar{X}$ for the given number of students is 27.

Learn more about the confidence intervals here:

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