1. Researcher is interested in if students who attend private high schools have higher average SAT Scores than students in the general population or not. Random sample of 90 students at a private high school is tested and mean SAT score of 1030 is obtained. Average score for public high school student is 1000 (σ= 200).
a. Is it one- or two tailed test?
b. Determine H0 and Ha for this study?
c. Evaluate Z obt
d. Determine Z critical value (Z cv ) using a 0.05 alpha level?
e. Should H0 be rejected? What should the researcher conclude?
f. Find the 95 % confidence interval for the population mean, based on the sample mean.
2. A researcher hypothesized that pulse rates of long-distance athletes vary from those of other athletes. He believed that runners’ pulses will be slower. He got 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. 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. Determine tcv from appendix A in Jackson’s text.
e. Calculate t obt
f. Should H0 be rejected? What must the researcher conclude?
3. A researcher hypothesizes that people who listen to music via headphones have greater hearing loss and would thus score lower on a hearing test than those in the general population. On standard hearing test, the overall mean for the general population is 22.5. Researcher gives this similar 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. Which statistical test should be used to analyze the data?
b. Is this a one- or two- tailed test?
c. Find H0 and Ha for this study?
d. Calculate t obt
e. Should H0 be rejected? What must the researcher conclude?