What does it mean? I need help with this

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) 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

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

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:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

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

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0

3 years ago

What is the difference between intermediate algebra and algebra 1?

Igoryamba

Algebra 1 just really teaches you the basics of algrebra

6 0

4 years ago

Read 2 more answers

How would the expression x^2-4 be rewritten using Difference of Squares?

Anna [14]

a2 – b2 = (a + b)(a – b) or (a – b)(a + b).
This is the 'Difference of Squares' formula we can use to factor the expression.

In order to use the 'Difference of Squares' formula to factor a binomial, the binomial must contain two perfect squares that are separated by a subtraction symbol.

x^2 - 4 fits this, because x^2 and 4 are both perfect squares, and they are separated by a subtraction symbol.
All you do here to factor, is take the square root of each term.

√x^2 = x
√4 = 2

Now that we have our square roots, x and 2, we substitute these numbers into the form (a + b)(a - b).

(a + b)(a - b)
(x + 2)(x - 2)

Our answer is final (x + 2)(x - 2), which can also be written as (x - 2)(x + 2), it doesn't make a difference which order you put it in.

Anyway, Hope this helps!!
Let me know if you need help understanding anything and I'll try to explain as best I can.

3 0

3 years ago

Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height

Elena L [17]

The amount of balloons in the tent is 125.075 feet cube. From the given options, approximately, option D is correct

Solution:

Given, Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height is 6.3 feet.

Rob filled the tent with balloons,

We have to find which measurement BEST describes the amount of balloons in the tent?

As tent if filled with balloons the amount of balloons equals with volume of tent.

Volume of tent is given as:

$\text { volume of tent }=a^{2}+2 a \sqrt{\frac{a^{2}}{4}+h^{2}}$

where "a" is side length and "h" is height.

$\begin{array}{l}{\text { Then, Volume }=6.3^{2}+2(6.3) \sqrt{\frac{6.3^{2}}{4}+6^{2}}} \\\\ {=39.69+12.6 \sqrt{9.925+36}} \\\\ {=39.69+12.6 \times 6.7766=39.69+85.385} \\\\ {=125.075 \mathrm{ft}^{3}}\end{array}$

Hence, from the given options, approximately, option D is correct.

6 0

3 years ago

Read 2 more answers

If a line has a slope of -4 and a u intercept of 1, which of the following is it's graph?

3241004551 [841]

Well. I can't see the picture. But it would be decreasing at a rate of 4 so pick a point on the any line move over to the right one, then down four. And for the y intercept the line would intersect the y axis at positive one. Sorry if that's confusing

3 0

3 years ago