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The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (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 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

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

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil

Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation $y=\frac{k}{x}$ represents the relation where y is inversely proportional to x and k is the constant of proportionality.

So our required equation would be $d=\frac{k}{n}$

Upon substituting our given values, we will get:

$19=\frac{k}{35}$

$k=19\cdot 35$

$k=665$

Since constant of proportionality is 665, so our equation would be $d=\frac{665}{n}$ .

To find the number of days it will take to build a similar house with 5 workers, we will substitute $n=5$ in our equation as:

$d=\frac{665}{5}$

$d=133$

Therefore, it will take 133 days for 5 workers to build a similar house.

5 0

3 years ago

What is the slope of the line perpendicular to a line that contains the points (-5,4) and (-2,4)

steposvetlana [31]

Answer:

the slope of the line is: 0

Step-by-step explanation:

4-4=0

-2-5= 3

7 0

3 years ago

Which is equivalent to 216 1/3? A.3 B.6 C.36 D.72

nydimaria [60]

The 1/3 power is another way to write the cube root.
∛216 = 6

3 0

3 years ago

for every 300 kids in high school 2/3 of them take a language. What is the value of a number of students who dont take a languag

Anna [14]

All you have to do is divide 300 hundred by 3 and you get 100 students that don’t take a language So 200 students take language and 100 students don’t take language

3 0

3 years ago