Help I cant figure out how to do this type of problem

The ages of a random sample of five university professors are 39, 54, 61, 72, and 59. Using this information, find a 99% confide

blsea [12.9K]

Answer:

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

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:

$6.237 \leq \sigma \leq 52.843$

3 0

3 years ago

Read 2 more answers

Find the area and perimeter of the composite shape below... WILL GIVE BRAINLIST FOR BEST ANSWER !!!

Ber [7]

Perimeter:

3+3+2+3+10+3+3+6+2+3=38

Perimeter is 38

Area:

Shape a: 3*3=9

Shape b: 3*5=15

Shape c: 10*3=30

30+15+9=54

Area is 54

3 0

4 years ago

Read 2 more answers

What is the answer ?

Tatiana [17]

Answer:

x is 30° and y is 150°

Step-by-step explanation:

x is 30° and y is 150°. These facts stem from the horizontal lines all being parallel and sharing a single transversal which creates the angles shown in this illustration.

6 0

4 years ago

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

marysya [2.9K]

Victoria is 9. Her neighbor is 5.

7 0

3 years ago

PLEASE HELP IM BEGGING Ira B. Scholar, that bizarre math teacher, put the figure at right on a recent test and said,

rewona [7]

Answer:

The perimeter is the distance all the way around the outside of a 2D shape. To calculate the perimeter, sum the lengths of all the sides.

Therefore, perimeter of the triangle = (2x - 8) + (2x + 5) + (30 - 3x)

Collect like terms: 2x + 2x - 3x - 8 + 5 + 30

Combine like terms: x + 27

Therefore, perimeter of triangle = x + 27

We are told that the perimeter is 25:

x + 27 = 25

Subtract 27 from both sides: x = -2

If x = -2, then the side with equation 2x - 8 = (2 x -2) - 8 = -12

A length cannot be negative, therefore the perimeter cannot equal 25.

7 0

3 years ago