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Tamy · Answer 1 · 2021-01-16T16:38:00+0000

Answer:

33.9-1.32(7.2)/(√(25))=31.999

33.9+1.32(7.2)/(√(25))=35.801

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_(\alpha/2)(s)/(√(n))$

And replacing we got:

ME = 1.32(7.2)/(√(25)) =1.9008

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".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

$\bar X \pm t_(\alpha/2)(s)/(√(n))$ (1)

In order to calculate the critical value
$t_(\alpha/2)$ we need to find first the degrees of freedom, given by:

df=n-1=25-1=24

Since the Confidence is 0.80 or 80%, the value of
$\alpha=0.2$ and
$\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that
$t_(\alpha/2)=1.32$

Now we have everything in order to replace into formula (1):