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)

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.