Mathematics, 07.04.2020 23:39, Caleb0018

The following measurements (in picocuries per liter) were recorded by a set of xenon gas detectors installed in a laboratory facility: 476,448.2,431.3 Using these measurements, construct a 99% confidence interval for the mean level of xenon gas present in the facility. Assume the population is approximately normal. Step 4 of 4 : Construct the 99% confidence interval. Round your answer to two decimal places.

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answered: oomale

$451.833-9.925\frac{22.570}{\sqrt{3}}=322.50$

$451.833+9.925\frac{22.570}{\sqrt{3}}=581.17$

So on this case the 99% confidence interval would be given by (322.50;581.17)

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 represent the sample size

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=451.833$

The sample deviation calculated s=22.570

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

df=n-1=3-1=2

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,2)".And we see that $t_{\alpha/2}=9.925$

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

$451.833-9.925\frac{22.570}{\sqrt{3}}=322.50$

$451.833+9.925\frac{22.570}{\sqrt{3}}=581.17$

So on this case the 99% confidence interval would be given by (322.50;581.17)

answered: Guest

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step-by-step explanation:

answered: Guest

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step-by-step explanation:

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