HELP FAST.

In a survey of 1000 women age 22 to 35 who work full time, 540 indicated that they would be willing to give up some personal in

morpeh [17]

Answer:

$z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.530$

$p_v =P(Z>2.530)=0.0057$

So 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 women indicated that they would be willing to give up some personal in order to make more money is significantly higher than 0.5.

The 95% confidence interval would be given by (0.509;0.571)

Step-by-step explanation:

Data given and notation

n=1000 represent the random sample taken

X=540 represent the women indicated that they would be willing to give up some personal in order to make more money

$\hat p=\frac{540}{1000}=0.54$ estimated proportion of women indicated that they would be willing to give up some personal in order to make more money

$p_o=0.5$ 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)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the majority of woman age 22 to 35 who work full-time would be willing to give up some personal time for more money.:

Null hypothesis: $p \leq 0.5$

Alternative hypothesis: $p > 0.5$

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 $p_o$ .

Calculate the statistic

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

$z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.530$

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 assumed is $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(Z>2.530)=0.0057$

So 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 women indicated that they would be willing to give up some personal in order to make more money is significantly higher than 0.5.

Confidence interval

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.54 - 1.96\sqrt{\frac{0.54(1-0.54)}{1000}}=0.509$

$0.54 + 1.96\sqrt{\frac{0.54(1-0.54)}{1000}}=0.571$

The 95% confidence interval would be given by (0.509;0.571)

5 0

3 years ago

In the division problem 18+ 3 = 6, is 18 the quotient divisor dividend remainder

MissTica

Answer:

Dividened

Step-by-step explanation:

Because that is what is going into 3

have a great day!

brailiest is appreciated!

8 0

3 years ago

Read 2 more answers

20% of a is 11. What is a?

a_sh-v [17]

Answer:

a is 5.

b is 16.

c is 24.

D is 9.

7 0

3 years ago

If 11250 = m(600) + b and 7650 = m(400) + b, how do I find the values of b and m? I forgot how to compare when I have two differ

Lelu [443]

Answer:

$b=450$ and $m=18$

Step-by-step explanation:

This exercise is an example of linear system equations. A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.

The easy way to solve this problem is by using the reduction method.The reduction method consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.

Ordering the equations as a system equations.

$\left \{ {{600m+b=11250} \atop {400m+b=7650}} \right.$

Using the reduction method, let's substract the second equation with the first equation, in order to clear m.

600m + b = 11250

-400m - b = -7650

200m = 3600 --------> m = 3600/200 -----> m = 18

We can substitute the value of m in any of the two equations to obtain the unknow b.

Let's substitute the value of m in the second equation.

400(18) + b = 7650

7200 + b = 7650 -----> b = 7650 - 7200 -------> b = 450

We can check this values in both equations.

600m + b = 11250 -----> 600(18) + 450 = 11250

400m + b = 7650 -----> 400(18) + 450 = 7650

Satisfying the result of both equations.

6 0

3 years ago

-7 2/3 +(5 1/2) + 8 3/4 =

drek231 [11]

Answer:

6 7/12

Step-by-step explanation:

-7 2/3 +(5 1/2) + 8 3/4

Get a common denominator of 12

-7 2/3 * 4/4 +(5 1/2 +6/6) + 8 3/4*3/3

-7 8/12 + 5 6/12 + 8 9/12

Subtract the first two terms first

They have opposite signs so subtract and take the sign of the larger

-7 8/12 + 5 6/12 = -2 2/12

-2 2/12 + 8 9/12

They have opposite signs so subtract and take the sign of the larger

-2 2/12 + 8 9/12 = 6 7/12

7 0

3 years ago