Question

3. The Idaho State University athletics department conducted a research study to see how many students attended a women’s lacrosse game last season. There are 14,400 students attending Idaho State University, and the study showed that 400 of 1250 students sampled attended a women’s lacrosse game. What inferences can be made about student attendance at women’s lacrosse 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?

PLEASE SHOW ALL WORK

Answer 1

ANSWER:

Given that,

a)

Estimated proportion = 400 / 1250 = 0.32

b)

95% confidence interval for p is

- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)

0.32 - 1.96 * sqrt( 0.32 * 0.68 / 1250) < p < 0.32 + 1.96 * sqrt( 0.32 * 0.68 / 1250)

0.32 - 1.96 *0.01319 < p < 0.3458

0.32 - 0.2585 < p < 0.3458

0.0615  < p < 0.3458

95% confidence interval is ( 0.0615 , 0.3458)

c)

The 99% confidence interval for p is

- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)

0.32 - 2.576 * sqrt( 0.32 * 0.68 / 1250) < p < 0.32 + 2.576 * sqrt( 0.32 * 0.68 / 1250)

0.32 - 2.576 * 0.01319 < p < 0.3539

0.32 -0.0339< p < 0.3539

0.2861< p < 0.3539

99% confidence interval is ( 0.2861 , 0.3539 )