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3 years ago

If |n| is a positive number, then n is a negative number. Which of the following would be a counterexample?

1 answer:

5 0

A counterexample for the following would be D, because it is the only positive number, which is opposite of a negative number.

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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 <u>Two-sample t test statistics</u> 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) <u><em>The test statistics</em></u> = $\frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }$ ~ $t_1_4$

= 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 <u>we fail to reject our null hypothesis</u>.

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

2 [ 32 - (4-1) to the third power ]

Tems11 [23]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

If you earned $60 from $500 in sales , What is the percent commission?

Rom4ik [11]

Answer:

300

Step-by-step explanation:

5 0

3 years ago

According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down

PSYCHO15rus [73]

Answer:

The required probability is 0.031918.

Step-by-step explanation:

Consider the provided information.

It is given that According to an article in The Wall Street Journal, this theory held for 22 out of the last 34 years.

Therefore n=34

The probability it is either up or down is 0.5.

Thus the value of p =0.5 and q = 0.5

Now calculate the probability

Let X is the number of years that theory held.

X has a binomial distribution with n=34 and p=0.5

$P(X=22)=\binom{34}{22}(0.5)^{22}(0.5)^{12}\\P(X=22)=\frac{34!}{22!\times 12!}(0.5)^{22}(0.5)^{12}\\P(X=22)=548354040\times 5.8207660913\times 10^{11}\\P(X=22)=0.0319184060208\\P(X=22)\approx0.031918$

Hence, the required probability is 0.031918.

8 0

3 years ago

You can use the formula S = 10m2/3 to approximate the surface area, S, in square centimeters, of a horse with mass m, in grams.

Vaselesa [24]

S = 10*m^(2/3)

S = 10*(450000)^(2/3)

S = 58,723.014617533

S = 58,723

<h3>Answer: Approximately 58,723 square cm.</h3>

4 0

3 years ago