10=c+d c is one more than d what is the value of c? with working out

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of Americans who decide to not go to college = 48%

n = sample of American adults = 331

p = population proportion of Americans who decide to not go to

college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\hat p-p$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ , $0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ ]

= [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

$0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }$

$\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}$

$\sqrt{n}$ = 54.79

n = $54.79^{2}$

n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

5 0

2 years ago

A square lawn has area 800ft^2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the

mestny [16]

I'm pretty sure your radius is 14.14'

3 0

2 years ago

Find f(x) if it is known that f(2a−1)=7a−13.

sattari [20]

Answer:

$f(x)=3.5x-9.5$

Step-by-step explanation:

Given:

The given function in terms of 'a' is given as:

$f(2a-1)=7a-13$

In order to determine $f(x)$ , we need to make $2a-1$ equal to 'x' and find the value of 'a'. Therefore,

$2a-1=x\\2a=x+1\\a=\frac{x+1}{2}$

Now, plug in the value of 'a' on both sides, we get:

$f(2\frac{x+1}{2}-1)=7\frac{(x+1)}{2}-13\\f(x+1-1)=3.5(x+1)-13\\f(x)=3.5x+3.5-13\\f(x)=3.5x-9.5$

Therefore, the expression for the function in terms of 'x' is:

$f(x)=3.5x-9.5$

6 0

2 years ago

The function f(x)=tan(3/2x-pi/2) has:

zlopas [31]

I think the best option here is B. period 2pi/3 and asymptote at x=0
because period of tanx is pi so period of tan(3/2x) is pi/(3/2) = 2pi/3. I hope this can work good for you.

3 0

2 years ago

5 Show different ways to make 492,623.

timama [110]

Step-by-step explanation:

Start by writing 492,623 in standard form

4 hundred thousands + 9 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones

We can write this in other ways by moving a digit to the next smaller place value. For example, we move the 4 one place to the right to get 49 ten thousands:

49 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones

Then, we can move the 49 ten thousands to the right to get 492 thousands, and we can move 6 hundreds to the right to get 62 tens.

492 thousands + 62 tens + 3 ones

Or, we can do this:

4926 hundreds + 23 ones

6 0

2 years ago

10=c+d c is one more than d what is the value of c?with working out