confidence interval problem?
A new technique for detecting breast cancer was correct in 229 out of 250 cases. Construct a 95% confidence interval for the true propotion correct rate. Report your answers in two differant ways.
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p-hat (I'll write capital P due to text restrictions) = 229/250 = 0.916
We are interested in the mean accuracy rate of a new technique for detecting breast cancer. Use the one proportion z-interval.
Conditions:
1) SRS: Assume SRS of 250 cases is given. Due to this assumption, proceed with caution.
2) Normality: nP = 250(0.916) = 229 > 10; n(1 - P) = 250(1 - 0.916) = 21 > 10. Therefore, the distribution of p-hat is approximately Normal.
3) Independence: population of cases > 10(250)
P ± z*√(P(1 - P)/n)
= 0.916 ± 1.96√(0.916(1 - 0.916)/250)
= 0.916 ± 0.03438534981
= (0.88161465018, 0.95038534981)
We are 95% confident that the mean accuracy rate falls between 0.8816 and 0.9504.