Atheletes at major colleges graduated on the whole at virtua

\"Atheletes at major colleges graduated, on the whole, at virtually the same rate as other students,\" according to the national collegiate athletic association. the survey involved students who had entered college before the NCAA\'s Proposition 48 took effect in 1985. Suppose that, in a new poll of 500 athletes at major colleges, the number graduating was 268. Find a 98% confidence interval for p, the proportion of athletes at major colleges who graduate and does the interval include the value p=.51, the graduation rate prior to prop 48? what do you conclude.

Solution

a.
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=268
Sample Size(n)=500
Sample proportion = x/n =0.536
Confidence Interval = [ 0.536 ±Z a/2 ( Sqrt ( 0.536*0.464) /500)]
= [ 0.536 - 2.326* Sqrt(0) , 0.536 + 2.33* Sqrt(0) ]
= [ 0.484,0.588]

b.
the interval include the value p=.51