What is used to locate points in the coordinate plane

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ 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 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }$ , $5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }$ ]

= [5.10 , 5.20]

Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0

3 years ago

I need help please i did not understand

antoniya [11.8K]

Answer:

Step-by-step explanation:

Add up all the values for the height and divide by 9. do the same for the leaf scars.

8 0

2 years ago

What is another solution of the equation x + y = 7?

White raven [17]

X=3, y=4
x=-2, y=9
Set x equal to anything, then isolate y to get the other number.

5 0

3 years ago

Which of the following graphs shows the preimage P(x)=x^2 and the image I(x)=P(1/3x)?

Ksju [112]

Answer:

The picture with the widest graph in red

Step-by-step explanation:

The graph P(x) is the parent graph for all quadratic functions. It has a vertex of (0,0) and has the following points:

x f(x)

-2 4

-1 1

0 0

1 1

2 4

The image of l(x) = P(1/3x) changes the points of the function to

x f(x)

-2/3 4/9

-1/3 1/9

0 0

1/3 1/9

2/3 4/9

This makes the graph much wider. The graph with the widest red graph is the graph.

7 0

3 years ago

Read 2 more answers

Please need help fast. Look at the picture. Please explain.

Zigmanuir [339]

The answer is 17

This is because 1 + 2 must equal 180 as they are in a straight line.
So 4x + 2 + 110 = 180
Take away 110 from both sides
4x + 2 = 70
Take away 2 from both sides to get 4x = 68. Finally, divide both sides by 4 to get x = 17

7 0

3 years ago