Solve the system using elimination. 3x – 3y = 24 2x + 2y = 4 The solution is |

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining wh

Molodets [167]

Answer:

(A) The mean for the differences is 2.0.

(B) The test statistic is 1.617.

(C) At 90% confidence the null hypothesis should not be rejected.

Step-by-step explanation:

We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.

The following data (in miles per gallon) show the results of the test;

Driver Manufacturer A Manufacturer B

1 32 28

2 27 22

3 26 27

4 26 24

5 25 24

6 29 25

7 31 28

8 25 27

Let $\mu_1$ = mean MPG for the fuel efficiency of Manufacturer A brand

$\mu_2$ = mean MPG for the fuel efficiency of Manufacturer B brand

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2=0$ or $\mu_1= \mu_2$ {means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2\neq 0$ or $\mu_1\neq \mu_2$ {means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}

The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n__1+_n__2-2$

where, $\bar X_1$ = sample mean MPG for manufacturer A = $\frac{\sum X_A}{n_A}$ = 27.625

$\bar X_2$ = sample mean MPG for manufacturer B = $\frac{\sum X_B}{n_B}$ = 25.625

$s_1$ = sample standard deviation for manufacturer A = $\sqrt{\frac{\sum (X_A-\bar X_A)^{2} }{n_A-1} }$ = 2.72

$s_2$ = sample standard deviation manufacturer B = $\sqrt{\frac{\sum (X_B-\bar X_B)^{2} }{n_B-1} }$ = 2.20

$n_1$ = sample of cars selected from manufacturer A = 8

$n_2$ = sample of cars selected from manufacturer B = 8

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(8-1)\times 2.72^{2}+(8-1)\times 2.20^{2} }{8+8-2} }$ = 2.474

(A) The mean for the differences is = 27.625 - 25.625 = 2

(B) The test statistics = $\frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }$ ~ $t_1_4$

= 1.617

(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.

5 0

3 years ago

If 8 boxes of crayons cost $20 , what would 6 boxes cost ?

Y_Kistochka [10]

Answer:

$15

Step-by-step explanation:

To figure thsi out, you do 20 divided by 8, which gives you 2.5 ($2.50.)

Next you do 2.50 x 6 which gives you 15 ($15.)

The answer is $15.

(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest. If my answer was wrong and you got marked wrong for it, I deeply apologize and hope you will forgive me, since everyone makes mistakes sometimes. If you need me to elaborate on my answer or give further explanation on it, please ask and I will do so. If you need to explain your reasoning on your work feel free to use my words- word for word- without crediting me, the answer was made for you anyways! Hope yall learn from my answer and it helps you in the future with assignments, quizzes, test’s, and more!

- •Trix•

( Yes I know my - •Trix• thingy is not my user but it’s what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)

6 0

3 years ago

Can someone please help me i literally am soo confused

Grace [21]

Answer:

a. Between 6.7 and 6.9

Step-by-step explanation:

√(25 + 3 + 17) = √45

6² = 36

7² = 49

√45 is close to 7 but slightly under. So best answer is A.

4 0

3 years ago

Which place do you round to find the rounded number that is closest to 9,760,000?

sukhopar [10]

You would round to the 100,000th place to find a rounded number closest to 9,760,000 because the 60,000 makes the 700,000 because an 800,000.

6 0

3 years ago

Based on a survey, assume that 32% of consumers are comfortable having drones deliver their purchases. Suppose that we want to

Nikolay [14]

Answer:

n = 6

x = 3

p = 0.32

q = 0.68

Step-by-step explanation:

Given:

32% are comfortable having drones deliver their purchases.

Suppose we are to find the probability that when 6 consumers are randomly selected, exactly 3 of them are comfortable with delivery by drones.

Required:

Find n, x, p, and q.

i) n represents the sample size. Here 6 consumers are selected randomly, therefore the sample size here is 6.

Thus, n = 6

ii) x represents the sample mean or number of successes. Since 3 consumers out of the selected 6 are comfortable with delivery by drones, the sample mean here is 3.

Thus, x = 3

iii) p represents population proportion or probability of success. Here population proportion(success probability) is 32% ≈ 0.32.

Thus, p = 0.32

iv) q represents probability of failure. To find probability of failure, use the formula:

1 - p

Thus,

1 - 0.32 = 0.68

q = 0.68

3 0

3 years ago

Solve the system using elimination.3x – 3y = 242x + 2y = 4The solution is |​

Solve the system using elimination.3x – 3y = 242x + 2y = 4The solution is |