If a diameter of a circle with a circumference of 104.48 mm is reduced by 1/2,what is the circumference of the new circle?

An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

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

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

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: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

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

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

3 years ago

Please answers all these questions for me need help too pass plz help☺

vodka [1.7K]

Please take 1 minute, and really read the example solution
under problem #12. All of the other eight problems on the
sheet are solved in exactly the same way:

Multiply each side of the equation by the denominator of
the fraction ... the number under the variable (the letter).

This easy step will get you the answer to each of the
eight problems.

I can't help noticing that the title of the sheet is 'extra PRACTICE' .
If someone handed you the answers, then you would not get the
practice. That would be just like stealing from you, and would be
just plain mean.

8 0

4 years ago

Pls help, I rlly need help.

riadik2000 [5.3K]

Answer:

AC = 15, CM = 20, CP = 12

Step-by-step explanation:

see the attached picture, I tried to explain as much as possible, the general idea is there are three triangles that are similar to one another and thus in proportion. Therefore you can find missing sides using ratios.

6 0

3 years ago

Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using th

kompoz [17]

Answer:

(h o k) (3) = 3

(k o h) (-4b) = -4b

Step-by-step explanation:

An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.

This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.

7 0

3 years ago

6. The ratio of girls to boys in an astronomy

mr Goodwill [35]

oksn ethe ansetware its 738wuy79q246978t59723482709uy783271-047892=-39074-2378904-2139047=123473192709270329742109372301790

Step-by-step explanation:

6 0

3 years ago