**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 average score for public high school student
is 1000 (?= 200).

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

b.
What
are H_{0} and H_{a} for this study?

c.
Compute
Z_{ obt}

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

e.
Should
H_{0} 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 runnersâ€™ 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 H_{0}and H_{a} for this study?

d.
Find
t_{cv} from appendix A in Jacksonâ€™s text.

e.
Compute
t _{obt}

f.
Should
H_{0} 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?

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

c.
What
are H_{0}and H_{a} for this study?

d.
Compute
t _{obt}

e.
Should
H_{0} be rejected? What should the researcher conclude?