You construct a confidence interval of the form 029493p04597

You construct a confidence interval of the form

0.29493p0.45978

from a sample of size 102 with 38 successes using the \"plus 4\" procedure.

Give the confidence level.

Solution

Margin of error = Confidence coefficient*Standard error of p
Confidence coefficient is the critical value of z (zc) for the level of confidence
Sample proportion = p = x/n = 38/102 = 0.37
Stadard error of p = sqrt [p*(1-p)/n]
= sqrt [0.37*0.63/102]
= 0.0478
Margin of error based on the confidential limits
= (upper limit - lower limit)/2
= (0.45978 - 0.29493)/2
= 0.082425
Therefore,
0.082425 = zc * 0.0478
zc = 0.082425/0.0478 = 1.7244
The confidence level corresponding to zc = 1.7244 is 95.73% approximately (you can find this value by using standard Z-tables )