Question

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

Answer 1

(a)Sample size Sample proportion Level of significanceC 450 given 0.47 0.05 given 95% level 1.96 from z table Two tailed critical value 2 | Za/2 Margin of error 2 0.0461 Lower limit 0.4239 Upper limit 0.5161 The 95% confidence interv (0.4239,0.5161)

(a)Sample size Sample proportion Level of significanceC 450 given 0.47 0.01 given 99% level za / 2 | 2.5758 from z table Two tailed critical value Za/2 Margin of error 2 0.0606 Lower limit 0.4094 Upper limit 0.5306 The 99% confidence interval is (0.4094,0.5306)

Answer 2

(.42,.52)

(.41,.53)