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…show more content…
The null hypothesis is that endurance runners’ pulse will either no difference than other athletes or will have a higher pulse than other athletes. The null and alternative hypothesis for the one-tailed directional test might more appropriately be written as H0:µ0 ≤ µ1, or µendurance runners’ pulse≤ µ Other Athletes Pulse Ha:µ0 > µ1, or µ endurance runners’ pulse> µ Other Athletes Pulse In other words, if the alternative hypothesis for a one-tailed test is µ0> µ1, then the null hypothesis is µ0 ≤ µ1, and to reject H0, the endurance runners’ have to have lower pulses than those of other athletes. d. Find tcv from appendix A in Jackson’s text.
Consulting Table A.3 (in Appendix A) for a one-tailed test with alpha = .05 and df = N – 1 = 9, tcv = 1.833.
e. Compute t obt t = X - µ / sx,sx= s/ Square Root of N
[MEAN] 45 + 45 + 64 + 50 + 58 + 49 + 47 + 55 + 50 + 52 = 515/10 = 51.5
6.0231 = SD
6.0231/sqrt10 = 6.0231/3.16 = 1.9
51.5 – 60/ 1.9 = - 4.47 = t
The sample mean falls - 4.47 standard deviations below the population mean of 60 [All calculations except for SD were done by using hand and/or 10 digit calculator.]
[SD calculator can be found here: http://easycalculation.com/statistics/standard-deviation.php] f. Should H0 be rejected? What should the researcher conclude? tobt= -