COUN 503 WEB CALCULATOR EXERCISE 2 Z test & One sample t-test 1. A resear cher is int erest ed in whether st udents wh o attend pri vate high sch ools have hi gher 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 t his a one- o r t wo tail ed t est ? b. What are H0 and Ha for this study? c. Compute Z obt d. What is t he Z critic al v alue (Z cv ) using a 0.05 alpha level? e. Should H0 be rejected? What should the researcher conclude? f. Deter mine t he 95 % confi dence in terva l for the pop ulati on mea n, based on the sample mean. 2. A resear cher hypot hesiz ed that the puls e rates of lon g-dist ance athl etes dif fer from t hose of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute. a. What stat isti cal t est s hould be us ed t o anal yze th e dat a? b. Is this a one- or two- tailed test? c. What are H 0 and H a for this study? d. Find t cv from appendix A in Jackson’s text. e. Compute t obt f. Should H0 be rejected? What should the researcher conclude? 3. A resear cher hypot hesiz es that peo ple who li sten to music via h eadphon es have gre ater hearing loss and will thus score lower on a hearing test than those in the general population. On a standard hearing test, the overall mean for the general population is 22.5. The researcher gives this same test to a random sample of 12 individuals who regularly use headphones. Their scores on the test are 15, 14, 20, 20, 25, 22, 21, 19, 16, 17, 21, 22. a. What stat isti cal t est s hould be us ed t o anal yze th e dat a? Page 1 of 2

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COUN 503

WEB CALCULATOR EXERCISE 2

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 averagescore for public high school student is 1000 (σ= 200).

a. Is this a one- or two tailed test?

b. What are H0 and Ha for this study?

c. Compute Z obt

d. What is the Z critical value (Z cv ) using a 0.05 alpha level?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95 % confidence interval for the population mean, based on the

sample mean.

2. A researcher hypothesized that the pulse rates of long-distance athletes differ from those of

other athletes. He believed that the runners’ pulses would be slower. He obtained a random

sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45,45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the

general population is normally distributed with a pulse rate of 60 beats per minute.

a. What statistical test should be used to analyze the data?

b. Is this a one- or two- tailed test?

c. What are H0 and Ha for this study?

d. Find tcv from appendix A in Jackson’s text.

e. Compute t obt

f. Should H0 be rejected? What should the researcher conclude?

3. A researcher hypothesizes that people who listen to music via headphones have greater hearing loss and will thus score lower on a hearing test than those in the general population.On a standard hearing test, the overall mean for the general population is 22.5. The

researcher gives this same test to a random sample of 12 individuals who regularly use

headphones. Their scores on the test are 15, 14, 20, 20, 25, 22, 21, 19, 16, 17, 21, 22.

a. What statistical test should be used to analyze the data?

Page 1 of 2