7x + 3 = 8x – 15 Need help please

In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

Data given and notation

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Part a: Test the hypothesis

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

Statistical decision 

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

6 0

3 years ago

Peter bought 15.5 yards of cord. He paid $0.40 per yard. How much did Peter spend on cord? A. $0.62 B. $6.20 C. $38.75 D. $62.00

mihalych1998 [28]

B $6.20 because you multiply 15.5x0.40

7 0

3 years ago

Read 2 more answers

It cost $9 to go to pete's Pottery place to make your own bowls for $3 per bowl. Natalie goes to Pete's Pottery place and makes

shusha [124]

A) total cost = 3b+(9*5)

B)

she makes 4 bowls every visit (5) so 5*4 = 20 total bowls

total cost = 3(20) +(9*5) = 60+45= 105 dollars

8 0

3 years ago

Question below in image

Arturiano [62]

Answer:

m=4 n=5

Step-by-step explanation:

2n-1 = 9 because 1 is negative you add it to the 9 so the equation becomes 2n=10 then divide 10 by 2 and you get n=5

m+8 = 3m subtract the lone m (or 1m) from the left to the 3m which gives you 2m=8 then divide 8 by 2 and you get m=4

plug in the numbers to check.

2n-1=9= (2x5)-1=9 | 10-1=9 | 9=9

m+8=3m= 4+8=(3x4) | 12=12

5 0

3 years ago

How do I solve this?

AleksAgata [21]

Answer:

x = -1

y = -1

Step-by-step explanation:

3x - y = -2

2x + y = -3

Multiply equation 1 by 2 and equation 2 by 3

We have

2x3x - 2xy = 2x-2

3x2x + 3xy = -3x3

Equation 1 6x - 2y =-4

Equation 2 6x + 3y = -9

Subtract equation 2 from 1

We have -5y = 5

Divide both sides by -5

y = 5/-5 = -1

Now Substitute y = -1 into any of the equations to get x

Using equation 1 , we have

3x - (-1) = -2

3x +1 = -2

Collect like terms

3x = -2 -1

3x = -3

Divide both sides by 3

x = -3/3 = -1

4 0

3 years ago

Read 2 more answers