Answer to Question #6467 in Statistics and Probability for carol
A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).
What is the Z critical value (Z cv ) using a 0.05 alpha level?
Should H0 be rejected? What should the researcher conclude?
Determine the 95 % confidence interval for the population mean, based on the sample mean.
Let Ho: average private high scools score (m)<=aver. general score (M). So we can use one-tailed z-test. z-score equals Z=(m-M)*sqrt(n)/σ=(1030-1000)*sqrt(90)/200=1.42 Z cv=1.645 (we take it from normal distribution table for alpha=0.05) Z<Z cv, so we can't reject Ho and conclude that the observed data set provides no strong evidence against the null hypothesis. The 95% confidence interval based on the sample mean (now we suppose that population mean is uknown with known standard deviation) is m±Z*σ/sqrt(n), where Z*=Z cv for level alpha/2 (! because to get an interval we need to use two-sided estimation). Z*=1.96 and 95% confidence interval is (1030-41.32;1030+41.32)=(988.68,1071.32)