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3 years ago

Declaration of Independence

1 answer:

8 0

The Declaration of Independence is defined as the formal statement written by Thomas Jefferson declaring the freedom of the thirteen American colonies from Great Britain. An example of the Declaration of Independence was the document adopted at the Second Continental Congress on July 4th, 1776

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"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

Let $p_1$ = proportion of drivers that were in compliance initially

$p_2$ = proportion of drivers that were in compliance one year later

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, the test statistics = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

Now, P-value of the test statistics is given by;

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = 0.00043

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

7 0

3 years ago

Plzzzzz help ASAP!!!!!!!!!

Alecsey [184]

I think it’s b the second one

5 0

3 years ago

Read 2 more answers

Type the integer that makes the following subtraction sentence true: -57 - ? = -151

posledela

Answer:

Step-by-step explanation:

Its pretty simple,

The easiest way to find the missing number is to do 151-57, which = 94

8 0

3 years ago

Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 a

Ahat [919]

Answer:

f(x) = (3x³ + 9x² - 27x + 15)/32

Step-by-step explanation:

f'(x) = 3ax² + 2bx + c

Maximum or minimum: f'(x) = 0

Maximum: f'(-3) = 0 and f(-3) = 3

Minimum: f'(1) = 0 and f(1) = 0

f'(-3) = 0 leads 27a - 6b + c = 0 (1)

f'(1) = 0 leads 3a + 2b + c = 0 (2)

f(-3) = 3 leads -27a + 9b -3c + d = 3 (3)

f(1) = 0 leads a + b + c + d = 0 (4)

(1) - (2): 24a - 8b = 0, or 3a - b = 0, b = 3a

(3) - (4) -28a + 8b - 4c = 3 (5)

(1) * 4 + (5): 80a - 16b = 3,

use b = 3a, get 80a - 16*3a = 3, 32a = 3, a = 3/32, b = 3a = 9/32

From (2): c = -3a - 2b = -9/32 - 18/32 = -27/32

From (4): d = -a - b - c = -3/32 - 9/32 + 27/32 = 15/32

f(x) = (3x³ + 9x² - 27x + 15)/32

3 0

2 years ago

PLEASE HELP! I am doing Imagine Math and I need help with this question!

Vaselesa [24]

The bottom left option is when it is reflected over the x axis, the second to last option on the left is when it is reflected of the y axis, and the middle option is when it is reflected over the line y = x

Hope this helps :)

5 0

2 years ago