Webcalc Ii
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? Key word “whether”.This is a two-tailed hypothesis test. Researcher wants to know “whether” the groups being compared differ, but does not predict the direction of the difference. The mean of the sample will be different from or unequal to the mean of the general population. b. What are H0 and Ha for this study? The researcher predicts a difference in SAT scores between private high schools and those in public high schools, but the direction of the difference is not predicted. Those in private high schools would be expected to have either higher or lower SAT scores but not the same SAT score as the public high schools. The statistical notation for this two-tailed test is H0:µ0 = µ1, or µPrivate High School = µ Public High School Ha:µ0 = µ1, or µPrivate High School ≠ µ Public High School c. Compute Zobt The mean SAT score of the public high school (µ) is 1000, with a standard deviation (σ) of 200; for private high school in the sample (N=90), mean SAT score is 1030. σx= σ/Square Root of N = 1000/Square Root of 200 = 1000/14.14 = 70.72 z= X - µ/σx= 1030 – 1000/70.72 = 30/70.72 = .42 Zobt= .42 [All calculations were done by using hand and/or 10 digit calculator.] d. What is the Z critical value (Z cv ) using a 0.05 alpha level? According to table A.2 0.05 alpha level is 1.96 e. Should H0 be rejected? What should the researcher conclude? Zobthas to be as large or larger than Z cvto reject H0 Zobt= .42 Z cv= 1.96 Zobt< Z cv, therefore H0 should be
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? Key word “whether”.This is a two-tailed hypothesis test. Researcher wants to know “whether” the groups being compared differ, but does not predict the direction of the difference. The mean of the sample will be different from or unequal to the mean of the general population. b. What are H0 and Ha for this study? The researcher predicts a difference in SAT scores between private high schools and those in public high schools, but the direction of the difference is not predicted. Those in private high schools would be expected to have either higher or lower SAT scores but not the same SAT score as the public high schools. The statistical notation for this two-tailed test is H0:µ0 = µ1, or µPrivate High School = µ Public High School Ha:µ0 = µ1, or µPrivate High School ≠ µ Public High School c. Compute Zobt The mean SAT score of the public high school (µ) is 1000, with a standard deviation (σ) of 200; for private high school in the sample (N=90), mean SAT score is 1030. σx= σ/Square Root of N = 1000/Square Root of 200 = 1000/14.14 = 70.72 z= X - µ/σx= 1030 – 1000/70.72 = 30/70.72 = .42 Zobt= .42 [All calculations were done by using hand and/or 10 digit calculator.] d. What is the Z critical value (Z cv ) using a 0.05 alpha level? According to table A.2 0.05 alpha level is 1.96 e. Should H0 be rejected? What should the researcher conclude? Zobthas to be as large or larger than Z cvto reject H0 Zobt= .42 Z cv= 1.96 Zobt< Z cv, therefore H0 should be