PLEASE DON'T GUESS! I NEED THE CORRECT ANSWER!!!! THIS IS A TEST!!!!

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

Notice that the margin of error decreases when the sample size increases.

4 0

3 years ago

Find the length of BC. A.) 14 B.) 9 C.) 2 D.) 3

Vera_Pavlovna [14]

Answer:

A) 14

Step-by-step explanation:

BC is congruent to DC in saying this you can plug the equations to each other and solve for y and then put its back into the equation for BC to get the length.

3y+5=5y-1

subtract 3y from both sides --> 5=2y-1

add 1 to both sides --> 6=2y

now get y alone, divide by 2 by both side --> y=3

plug y in back to 5y-1 --> 5x3-1

15-1

BC = 14

7 0

3 years ago

Steps to solve a two step equation

Kobotan [32]

I'm not entirely sure about some of these because there could be multiple answers, i think. i'll just leave the ones i can't help you with blank.

1) Begin to (isolate) the (variable) by eliminating the (constant). To eliminate the constant, you want to make it (cancel?) because ___+___=___)
2) (Balance) your equation by doing the exact same thing in the opisite side of the (equal sign).
3) Finish (isolating) the (variable) by eliminating the (coefficient). To eliminate the coefficient, you want to make it (cancel?) because ___x___=___,
4) (Balance) your equation by doing the exact same thing on the opposite side of the (equal sign).
5) Check your answer by (plugging) it in or the _____.

honestly, i find it really amusing that they found a way to break a TWO-step equation into 5 steps ?? but i hope this helps a little!!

7 0

3 years ago

Two lines and a point are guaranteed to be coplanar If..

Roman55 [17]

Two lines and a point are guaranteed to be coplanar if the two lines share only a single point.

Hope this helped :)

8 0

4 years ago

Read 2 more answers

Which graph or equation represents a nonproportional relationship?

Brut [27]

The graph that does not represents a proportional relationship is: A (see image attached below).

<h3>What is a Proportional Relationship?</h3>

A proportional relationship has a constant, which is uniform and is defined in the equation y = kx, as k. This means a relationship that is proportionate will have an equation in that form.

For a proportional graph, the line must pass through the point of origin which is denoted by the ordered pair, (0, 0).

Therefore, from the options given, the option B represents a proportional relationship because it contains (0, 0), while option C and D takes the form of y = kx.

Therefore, option A does not represent a proportional relationship.

Learn more about proportional relationship on:

brainly.com/question/15618632

#SPJ1

5 0

2 years ago

Read 2 more answers