For options A-E choose all of the expressions that are equivalent to 3(4x + 3).

A survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked,

katovenus [111]

Answer:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

Step-by-step explanation:

Data given and notation

$X_{1}=45$ represent the number of correct answers for university degree holders

$X_{2}=57$ represent the number of correct answers for university non-degree holders

$n_{1}=373$ sample 1 selected

$n_{2}=639$ sample 2 selected

$p_{1}=\frac{45}{373}=0.121$ represent the proportion of correct answers for university degree holders

$p_{2}=\frac{57}{639}=0.0892$ represent the proportion of correct answers for university non-degree holders

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different between the two groups, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{45+57}{373+639}=0.101$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

7 0

3 years ago

Which is the slope of the line that passes through the points (3,5) and (8,7)?

Hatshy [7]

Hi there!

»»————-　★　————-««

I believe your answer is:

$m=\boxed{\frac{2}{5}}$

»»————-　★　————-««

Here’s why:

The formula for the slope of two given lines given is 'rise over run'.

⸻⸻⸻⸻

$\boxed{\text{Slope Formula:}}\\\\\frac{y_2-y_1}{x_2-x_1}\\\\\rightarrow (x_1,y_1),(x_2,x_1) - \text{Two Points Given}$

⸻⸻⸻⸻

We are given the points (3,5) and (8,7).

⸻⸻⸻⸻

$\boxed{\text{Finding the Slope:}}\\\\\rightarrow m=\frac{7-5}{8-3}\\\\\rightarrow \boxed{m=\frac{2}{5}}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

7 0

3 years ago

15. Madison invested in a certificate of deposit for 4 years at a 6% interest rate. At the end of the 4 years, the value

Reptile [31]

Answer:

2455.49

Step-by-step explanation:

$3100=x(1+.06)^4\\x=2455.490356$

6 0

3 years ago

Carmen represents the equation y=x^2+1 using a graph. She says her graph shows there is more than one input for almost every out

Korvikt [17]

No - It is a function.

A relation which is not a function has more than 1 output for an input.

7 0

3 years ago

In January 2011 the rate of a VAT increased from 17.5% to 20% Work out the difference in price of a car worth £15000 + VAT due t

Jobisdone [24]

Answer:

£375

Step-by-step explanation:

The tax changed from 17.5% of the car's price to 20% of the car's price, an increase of 2.5% of the car's price.

The increased tax amount is ...

0.025 × £15000 = £375

The price of the car went up by £375 due to the increase in VAT.

3 0

3 years ago