3. * + 4y = 6 = -x +3 What is the answer

A sample of 200 observations from the first population indicated that X1 is 170. A sam- ple of 150 observations from the second

nikitadnepr [17]

Answer:

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

$p_1=X_1/n_1=170/200=0.85$

The sample 2, of size n2=150 has a proportion of p2=0.7333.

$p_2=X_2/n_2=110/150=0.7333$

The difference between proportions is (p1-p2)=0.1167.

$p_d=p_1-p_2=0.85-0.7333=0.1167$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z>2.7)=0.0072$

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

6 0

2 years ago

Identify the slope and the y-intercept of the linear equation. Y=4x+7

Thepotemich [5.8K]

Answer:

Hey there!

The slope of the line is 4, and the y-intercept is (7,0)

Let me know if this helps :)

6 0

2 years ago

Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean)

natka813 [3]

Answer:

Afternoon class has more students.

Step-by-step explanation:

Let m be the number of students in the morning class and n be the number of students in the afternoon class.

The average score for the students in the morning class was 80, then the sum of their scores is $80m.$

The average score for the students in the afternoon class was 86, then the sum of their scores is $86n.$

The sum of the scores of both classes is

$80m+86n$

and the average score is

$\dfrac{80m+86n}{m+n}$

The average (arithmetic mean) score for the two classes combined was 84, then

$\dfrac{80m+86n}{m+n}=84\\ \\ 80m+86n=84m+84n\\ \\86n-84n=84m-80m\\ \\2n=4m\\ \\n=2m$

This means n is greater, so afternoon class has more students.

7 0

2 years ago

Write this number in expanded form in the box below. Use powers of ten in your answer.

yarga [219]

Answer:

3000+400+30+9+0.30+0.06, very simple

Step-by-step explanation:

no need

5 0

2 years ago

Read 2 more answers

First one right gets BRAINLIEST!! If f(x)=x²+2x-3 and g(x)=x²-9, find (f/g) 4 and (f+g)(4)

Rasek [7]

Answer:

3 and 28

Step-by-step explanation:

note ( $\frac{f}{g}$ )(x ) = $\frac{f(x)}{g(x)}$

$\frac{f(x)}{g(x)}$

= $\frac{x^2+2x-3}{x^2-9}$ and

( $\frac{f}{g}$ )(4) = $\frac{4^2+2(4)-3}{4^2-9}$ = $\frac{16+8-3}{16-9}$ = $\frac{21}{7}$ = 3

-------------------------------------------------------

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= x² + 2x - 3 + x² - 9 = 2x² + 2x - 12 and

(f + g)(4) = 2(4)² + 2(4) - 12 = 2(16) + 8 - 12 = 32 + 8 - 12 = 28

6 0

2 years ago