3. The University of Chicago conducted a study to see how many students attended a women’s softball game last season. There are 14,400 students attending NC State University, and the study showed that 450 of 900 students sampled attended a women’s soccer game. What inferences can be made about student attendance at women’s softball games? (a) What is the estimated proportion for the population? (b) Using the 95% level of confidence, what is the confidence interval? (c) Using the 99% level of confidence, what is the confidence interval?
a)
Estimated proportion = 450 / 900 = 0.50
b)
95% confidence interval for p is
- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)
0.5 - 1.96 * sqrt( 0.5 * 0.5 / 900) < p < 0.5 + 1.96 * sqrt( 0.5 * 0.5 / 900)
0.467 < p < 0.533
95% confidence interval is ( 0.467 , 0.533)
c)
The 99% confidence interval for p is
- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)
0.5 - 2.576 * sqrt( 0.5 * 0.5 / 900) < p < 0.5 + 2.576 * sqrt( 0.5 * 0.5 / 900)
0.457 < p < 0.543
99% confidence interval is ( 0.457 , 0.543 )
Get Answers For Free
Most questions answered within 1 hours.