Question

The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 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. (to 2 decimals)

b. Provide a 99 % confidence interval for the population proportion of college students who work to pay for tuition and living expenses. (to 2 decimals)

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b. Provide a  confidence interval for the population proportion of college students who work to pay for tuition and living expenses. (to 2 decimals)

Answer 1

Solution:

a) The 95% confidence interval for population proportion is given as follows:

Where, p̂ is sample proportion, q̂ = 1 - p̂, n is sample size and Z(0.05/2) is critical z-value to construct 95% confidence interval.

Sample proportion of college students who work to pay for tuition and living expenses is, p̂ = 47% = 0.47

q̂ = 1 - 0.47 = 0.53 and n = 450

Using Z-table we get, Z(0.05/2) = 1.96

Hence, 95% confidence interval for population proportion is,

The 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses is (0.42, 0.52).

b) The 99% confidence interval for population proportion is given as follows:

Where, p̂ is sample proportion, q̂ = 1 - p̂, n is sample size and Z(0.01/2) is critical z-value to construct 99% confidence interval.

Sample proportion of college students who work to pay for tuition and living expenses is, p̂ = 47% = 0.47

q̂ = 1 - 0.47 = 0.53 and n = 450

Using Z-table we get, Z(0.01/2) = 2.576

Hence, 99% confidence interval for population proportion is,

The 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses is (0.41, 0.53).