The National Center for Education Statistics reported that of college students work to pay for tuition and living expenses. Assume that a sample of college students was used in the study. A. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. B. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. C. What happens to the margin of error as the confidence is increased from 95% to 99%?

A) = 0.0235

B) = (0.4095, 0.5305)

C) = With increase in confidence from 95% to 99%, also comes with increase in the margin of error and width of the confidence interval.

Step-by-step explanation:

Step 1:

size of random sample (n) = 450

Percentage of student working to pay tuition = 47%

Proportion of student working to pay tuition (P) = 0.47

Estimating the Standard error, /

substituting the data in the above equation and solving will give 0.0235

Step 2:

For a 95% confidence, the confidence coefficient is 1 - ∝ = 0.95   ∴  ∝ = 0.05.

Using standard normal area table, ∝/2 = 0.05/2 = 0.025

Z (∝/2) = Z (0.025) = 1.96

95% confidence interval

P±Z(∝/2) *

= 0.47±1.96(0.025)

= 0.47±0.0461

= (0.4239, 0.5161)

Step 3:

For a 99% confidence, the confidence coefficient is 1 - ∝ = 0.99   ∴  ∝ = 0.01

Using standard normal area table, ∝/2 = 0.01/2 = 0.005

Z (∝/2) = Z (0.005) = 2.576

99% confidence interval

P±Z(∝/2) *

= 0.47±2.576(0.0235)

= 0.47±0.0605

= (0.4095, 0.5305)

Step 4:

Observe that it is on the increase.

1. at 95%, confidence intervals are (0.4239, 0.5161)

2. at 99%, confidence intervals are (0.4095, 0.5305)

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

so then what are you asking?

step-by-step explanation: