Mathematics, 02.03.2020 21:17 catherinethomas0826

The ages of a random sample of five university professors are 39, 54, 61, 72, and 59. Using this information, find a 99% confidence interval for the population standard

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Answer from: lilroach4

$38.898 \leq \sigma^2 \leq 2792.356$

Now we just take square root on both sides of the interval and we got:

$6.237 \leq \sigma \leq 52.843$

Step-by-step explanation:

Data given and notation

34,59,61,71,59

We can calculate the sample standard deviation with the following formula:

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

$s= \sqrt{s^2}$

s=12.021 represent the sample standard deviation

$\bar x$ represent the sample mean

n=5 the sample size

Confidence=99% or 0.99

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=5-1=4

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 values.

The excel commands would be: "=CHISQ.INV(0.005,4)" "=CHISQ.INV(1-0.005,4)". so for this case the critical values are:

$\chi^2_{\alpha/2}=14.860$

$\chi^2_{1- \alpha/2}=0.207$

And replacing into the formula for the interval we got:

$\frac{(4)(12.021)^2}{14.860} \leq \sigma^2 \leq \frac{(4)(12.021)^2}{0.207}$

$38.898 \leq \sigma^2 \leq 2792.356$

Now we just take square root on both sides of the interval and we got:

$6.237 \leq \sigma \leq 52.843$

Answer from: Quest

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.

Answer from: Quest

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

~just a girl in love with shawn mendes

Find the composition of transformations that map abcd to ehgf. !

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The ages of a random sample of five university professors are 39, 54, 61, 72, and 59. Using this inf...