If a ll b and line c is perpendicular to line a then line b and c are?

A statistician is testing the null hypothesis that exactly half of all engineers will still be in the profession 10 years after

lana [24]

Answer:

95% confidence interval estimate for the proportion of engineers remaining in the profession is [0.486 , 0.624].

(a) Lower Limit = 0.486

(b) Upper Limit = 0.624

Step-by-step explanation:

We are given that a statistician is testing the null hypothesis that exactly half of all engineers will still be in the profession 10 years after receiving their bachelor's.

She took a random sample of 200 graduates from the class of 1979 and determined their occupations in 1989. She found that 111 persons were still employed primarily as engineers.

Firstly, the pivotal quantity for 95% 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 persons who were still employed primarily as engineers = $\frac{111}{200}$ = 0.555

n = sample of graduates = 200

p = population proportion of engineers

Here for constructing 95% confidence interval we have used One-sample z proportion test statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of

significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.555-1.96 \times {\sqrt{\frac{0.555(1-0.555)}{200} } }$ , $0.555+1.96 \times {\sqrt{\frac{0.555(1-0.555)}{200} } }$ ]

= [0.486 , 0.624]

Therefore, 95% confidence interval for the estimate for the proportion of engineers remaining in the profession is [0.486 , 0.624].

7 0

3 years ago

What are 3 different equations that have x=5 as a solution

Zepler [3.9K]

Answer:

1) x+y=50

2) 5x+2y=200

3)2x+4y=200

Hope this helps!

8 0

3 years ago

Read 2 more answers

You have 108 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the River

Licemer1 [7]

Answer:

The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.

Step-by-step explanation:

Given that,

The length of fencing of the rectangular plot is = 108 ft.

Let the longer side of the rectangular plot be x which is also the side along the river side and the width of the rectangular plot be y.

Since the fence along the river does not need.

So the total perimeter of the rectangle is =2(x+y) -x

=2x+2y-y

=x+2y

So,

x+2y =108

⇒x=108 -2y

Then the area of the rectangle plot is A = xy

A=xy

⇒A= (108-2y)y

⇒ A = 108y-2y²

A = 108y-2y²

Differentiating with respect to x

A'= 108 -4y

Again differentiating with respect to x

A''= -4

For maximum or minimum, A'=0

108 -4y=0

⇒4y=108

$\Rightarrow y=\frac{108}{4}$

⇒y=27.

$A''|_{y=27}=-4$

Since at y= 27, A''<0

So, at y=27 ft , the area of the rectangular plot maximum.

Then x= (108-2.27)

=54 ft.

The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.

3 0

3 years ago

What INVERSE OPERATION is used to solve the equation x/7=5?

VashaNatasha [74]

Answer:

Multiplying by 7 should solve

Step-by-step explanation:

To isolate x and solve the equation you multiply both sides by 7. x/7 cancels out to just x and 5 becomes 35

4 0

3 years ago

Which equation is correct regarding the measure of ∠mnp? m∠mnp = one-half(x – y) m∠mnp = one-half(x y) m∠mnp = one-half(z y) m∠m

Blababa [14]

Answer:

The measure of anle MNP is

m ∠ MNP = (x - y)/2

Explanation:

The image attached shows the figure corresponding to this question.

The angle MNP, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.

Then, you can use the theorem:

the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.

The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:

m ∠ MNP = (x - y)/2

6 0

2 years ago

If a ll b and line c is perpendicular to line a then line b and c are?​

If a ll b and line c is perpendicular to line a then line b and c are?