Evaluate: 100(1 - 0.02)10. Round to the nearest tenth.

4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B

AleksAgata [21]

Answer:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

Step-by-step explanation:

1) Data given and notation

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

$\hat p=\frac{63}{200}=0.315$ estimated proportion of lawyers had used some form of advertising for their business

$p_o=0.25$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that more than 25% of all the lawyers in Boston advertise for their business:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

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 $p_o$ .

3) Calculate the statistic

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

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about 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 $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

8 0

3 years ago

Sum of 2 and 5 is divided by the difference of 9 and 4 in expression form

Goshia [24]

Answer:

(2 + 5) / (9 - 4)

Step-by-step explanation:

"sum of 2 and 5" = (2 + 5)

"difference of 9 and 4" = (9 - 4)

"sum of 2 and 5 is divided by the difference of 9 and 4"

= (2 + 5) / (9 - 4)

5 0

3 years ago

The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x −4 The graph of g(x) is obtained by shifting down the g

Slav-nsk [51]

Correct Answer:
Option A

Solution:

f(x) = 7x + 9
g(x) = 7x - 4

We can re-write g(x) as:

g(x) = 7x + 9 - 13

Since 7x+9 is equal to f(x), we can write:

g(x) = f(x) - 13

This relation shows that g(x) is obtained by shifting f(x) 13 units vertically down. So the correct answer is option A.

6 0

3 years ago

Two sides of a triangle measure 14 inches and 8 inches. which cannot be the length of the remaining side?

horrorfan [7]

1. The "triangle inequality" states that any of the sides of the triangle, is larger than the difference of the other 2 sides (the larger minus the smaller), and it is smaller than the sum of them.

2. So the third side of this triangle must be larger than 14-8=6 (in) and smaller than 14+8=22 (in)

3. So let a denote the remaining side, then 6 < a < 22, which means a can be any number in between 6 and 22 inches.

3 0

3 years ago

How do I solve proportions? Here’s my questions: 1. x/8=5/16 2. 5/12=15/x

Flura [38]

Proportions are very simple once you get the hang of them! What you do is cross multiple. :)

1. x/8=5/16

You first start by multiplying x and 16

Then multiply 5 and 8

So now you have 16x=40

Finally divide 16 from each side

You get: x+0.4!

2. 5/12=15/x

Remember to cross-multiply!

Now we have 5x=180

Next divide 5 from each side

You get: x=36!

7 0

3 years ago