Mathematics, 18.03.2021 01:10 chrisraptorofficial

A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Required:
What represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?

Answers: 2

Show answers

Answers

The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)

Step-by-step explanation:

Subtraction of normal variables:

When we subtract the normal distributions, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

45 owners of newer cars (less than five years old). The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46

This means that:

$\mu_N = 195$

$s_N = \frac{46}{\sqrt{45}} = 6.8573$

40 owners of older cars (more than five years old). For older cars, the mean was $286 with a standard deviation of $58.

This means that:

$\mu_O = 286$

$s_O = \frac{58}{\sqrt{40}} = 9.17$

Subtaction:

Sample mean:

$\mu = \mu_N - \mu_O = 195 - 286 = -91$

Standard error:

$s = \sqrt{s_N^2 + s_O^2} = \sqrt{6.8573^2+9.17^2} = 11.45$

Confidence interval:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of 1 - 0.025 = 0.975 , so Z = 1.96.

Now, find the margin of error M as such

M = zs

In which s is the standard error.

M = zs = 1.96*11.45 = 22.44

The lower end of the interval is the sample mean subtracted by M. So it is -91 - 22.44 = -$113.44

The upper end of the interval is the sample mean added to M. So it is -91 + 22.44 = -$68.56

The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)

Answer from: Quest

answer: are you

step-by-step explanation:

Answer from: Quest

idk lol xd

step-by-step explanation:

ez do it yourself lazy

Another question on Mathematics

Mathematics, 21.06.2019 13:10

Plz which expression is equivalent to the expression below?

Answers: 1

Answer

Mathematics, 21.06.2019 15:20

Beth took out a $20,000 loan for college she is borrowing money from two banks. bank a charges an interest rate of 8.5% bank b charges and interest rate of 10.5% after one year alice owes $1860 in interest how much money did she borrow from bank a

Answers: 3

Answer

Mathematics, 21.06.2019 15:30

What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? assume that the cards are not replaced.

Answers: 2

Answer

Mathematics, 21.06.2019 16:30

Jorge planted flowers in his garden he planted one row of 12 tulips and one row of 36 daisies george's friend kylie has a garden with 75 flowers in it kylie's garden only contains tulips and daisies. is it possible for kylie‘s garden she have the same ratio of tulips to daisies as george's garden?

Answers: 1

Answer

You know the right answer?

A national consumer agency selected independent random samples of 45 owners of newer cars (less than...

Questions

Mathematics, 25.06.2019 08:00

Ill give u brainliest plzz i do flvs what is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied...