Question

In a sample of 100 college graduates, 85 get jobs within 3 months of graduation. Using z values, do the following: (a) Find a 95 percent confidence interval for the population proportion of new graduates that find a job within 3 months. Interpret the result. (b) Find a 99 percent confidence interval for the population proportion of new graduates that find a job within 3 months. Interpret the result.

Answer 1

= 85/ 100 = 0.85, 1 - = 0.15, n = 100

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The 95% CI, = 0.05

The Zcritical (2 tail) for = 0.05, is 1.96

The Confidence Interval is given by ME, where

The Lower Limit = 0.85 - 0.07 = 0.78

The Upper Limit = 0.85 + 0.07 = 0.92

The Confidence Interval is (0.78 , 0.92)

Interpretation: We are 95% confident that the true population proportion for all college graduates who get a job within 3 months of graduation lie between the limits 0.78 to 0.92

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The 99% CI, = 0.01

The Zcritical (2 tail) for = 0.01, is 2.576

The Confidence Interval is given by ME, where

The Lower Limit = 0.85 - 0.09 = 0.76

The Upper Limit = 0.85 + 0.09 = 0.94

The Confidence Interval is (0.76 , 0.94)

Interpretation: We are 99% confident that the true population proportion for all college graduates who get a job within 3 months of graduation lie between the limits 0.76 to 0.94

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