Z test & One sample t-test
1. 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).
a. Is this a one- or two tailed test?
This test is a one – tailed test, because the researcher wants to know that students who attend private high school will have a higher Sat score, which makes the alternative hypothesis a prediction in favor of the private school over the public high school.
b. What are H0 and Ha for this study?
The Hₒ foe the study is that the mean of the private school will be less than the mean from the public school. The Hₐ for this study is that the mean of the public school is higher than the mean for the public school.
c. Compute Z obt
To compute the Z obt we take the 200 which is the standard diviation and the 90 which is the sample size and plug in to the formula for standard error: 200divided by the square root of 90 = 21.082
d. What is the Z critical value (Z cv ) using a 0.05 alpha level?
Z cv for 005 alpha level is -1.6449
e. Should H0 be rejected? What should the researcher conclude?
H0 should not be rejected because there is not a large difference between both means.
f. Determine the 95 % confidence interval for the population mean, based on the sample mean.
Confidence level for population mean is less than 988.680 and higher than 1071.320 http://easycalculation.com/statistics/confidence-limits-mean.php
2. A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He...