# In a survey of 1016 ?adults, a polling agency? asked, "When you? retire, do you think you will have enough money to live comfortably or not. Of the 1016 ?surveyed, 535 stated that they were worried about having enough money to live comfortably in retirement. Construct a 99?% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.A. There is a 99?% probability that the true proportion of worried adults is between ___ and ___.B. 99?% of the population lies in the interval between ___ and ___.C. There is 99?% confidence that the proportion of worried adults is between ___ and ___.

C. There is 99% confidence that the proportion of worried adults is between 0.487 and 0.567

Step-by-step explanation:

1) Data given and notation

n=1016 represent the random sample taken

X=535 represent the people stated that they were worried about having enough money to live comfortably in retirement

estimated proportion of people stated that they were worried about having enough money to live comfortably in retirement

represent the significance level

Confidence =0.99 or 99%

z would represent the statistic

p= population proportion of people stated that they were worried about having enough money to live comfortably in retirement

2) Confidence interval

The confidence interval would be given by this formula

For the 99% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.

And replacing into the confidence interval formula we got:

And the 99% confidence interval would be given (0.487;0.567).

There is 99% confidence that the proportion of worried adults is between 0.487 and 0.567

To build a 99% confidence interval, we first calculate our sample proportion by dividing the number of such instances by the total sample size. Next, we determine the standard error of the proportion, then our margin of error by multiplying the standard error by the Z value of the selected confidence level. Lastly, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion.

### Explanation:

To construct a 99% confidence interval for the proportion of adults worried about having enough money to live comfortably in retirement, we will utilize statistical methods and proportions. First, we must calculate the sample proportion. The sample proportion (p) is equal to 535 (the number who are worried) divided by 1016 (the total number of adults surveyed).

Then, we find the standard error of the proportion which we get by multiplying the square root of ((p*(1-p))/n) where n is the number of adults sampled. The margin of error is found using the Z value corresponding to the desired confidence level, in this case, 99%. Multiply the standard error by this Z value. Lastly, we construct the confidence interval by taking the sample proportion (p) ± the margin of error.

The result will give you the 99% confidence interval - meaning we are 99% confident that the true proportion of adults who are worried about having enough money to live comfortably in retirement lies within this interval.

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## Related Questions

Pre Calc Introduction to Derivatives-Using Limits Help!

Attachment 1 : Option A,

Attachment 2 : Option D,

Attachment 3 : Option B,

Attachment 4 : Instantaneous rate of change will be 24

Step-by-step explanation:

"Remember that we can solve such questions by finding the derivative first"

1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.

The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.

2 : f'(5) = - 2 * 5 + 4,

f'(5) = - 10 + 4 = - 6

3 : f'(2) = 12 / 2 + 1 / - 3,

f'(2) = 12 / 3 / - 3 = 4 / - 3,

f'(2) = - 4 / 3

4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of  g.

g'(t) = 3(2x¹) + 0 = 6t,

And now we can evaluate the derivative at that value of  t.

g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24

How many pairs of skis in stock does the shop have to have to make the probability in question 4 less than .01? Round your answer to a whole numbermean=150
Standard Deviation=20

159 hwqb Step-by-step explanation:2n3wq,brudj32nwqrdb3wndj32wsd

You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Step-by-step explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.

0.00000000005 in scientific notation

It can be written as 5 x 10^ -11 or 0.5 x 10^ -10

Hope it helps.

Two equivalents of 7/4

14/8        21/12

Step-by-step explanation:

Explain how to use the distributive property to find an expression that is equivalent to 20+10