Hypothesis Test of Mean


Example: A sample of size 200 has a mean
of 20. Assume the population standard deviation is 6. Use the TI83
calculator to test the hypothesis that the population mean is not different
from 19.2 with a level of significance of α = 5%.
Solution: “The population mean is
not different from 19.2” means the same as “the population mean is equal to
19.2.” Therefore, the null and alternate hypotheses are H_{0}:
µ
= 19.2 and H_{1}: µ ≠ 19.2, respectively. Follow the steps below
to solve the problem using the TI83. [NOTE: If the pvalue < α,
reject the null hypothesis; otherwise, do not reject the null hypothesis.] 

Press STAT and the right arrow twice to select TESTS. To select
the highlighted

Use right
arrow to select Stats (summary values rather than raw data) and Press ENTER. Press down arrow to select Calculate and press ENTER. 
Results: Since the
pvalue is 0.1, do not reject the null hypothesis with an
α (alpha) value of 0.10 or smaller (10% level of
significance or smaller). [In this example, α = 0.05.] 
Hypothesis Test of Mean


Example: Two samples were taken, one from
each of two populations. Use the TI83 calculator to test the
hypothesis that the two population means are not different with a level of
significance of α = 5%.
Solution: For the two samples, we have the
following summary data:
“The two population means are not different” means the same as “the two population means are equal.” Therefore, the null and alternate hypotheses are H_{0}: µ_{1 }= µ_{2} and H_{1}: µ_{1 }≠_{ }µ_{2}, respectively. Follow the steps below to solve the problem using the TI83. [NOTE: If the pvalue < α , reject the null hypothesis; otherwise, do not reject the null hypothesis. 

Press STAT and the right arrow twice to select TESTS. Use the
down arrow to select

Use right
arrow to select Stats (summary values rather than raw data). Enter
standard deviations, mean and sample size for samples 1 and 2. Press
down arrow to select Calculate and press ENTER.

Results: Since the
pvalue is 0.0186, reject the null hypothesis with an alpha value of 0.05 or
larger (5% level of significance or larger). Conclude
that the two population means are not different. 
Hypothesis Test of Proportion


Example:
In sampling 200 people, we found that 30% of them favored a certain
candy. Use α = 10% to test
the hypothesis that the proportion of people who favored that candy is less
than 35%.


Press STAT and the right arrow twice to select TESTS. Use the
down arrow to select Press
ENTER.


Enter
hypothesized proportion, number of favorable outcomes, x, sample size, n, and
select the alternate hypothesis. Use down
arrow to select Calculate and press ENTER. 

Results: Since the
p = 0.069 is less than α = 0.10, reject the null ypothesis. Conclude that the sample proportion of
0.30 is significantly less than the hypothesized proportion of 0.35. 

Hypothesis Test of Proportion


Example:
In sampling 200 freshman college students (Sample 1), we found that 61 of
them earned an A in statistics. A sample of 250 sophomore college
students (Sample 2) had 60 people who earned an A in statistics. Test
the hypothesis that the proportion of freshmen that earned an A in statistics
is greater than the proportion of sophomores that earned an A in statistics.


Press STAT and the right arrow twice to select TESTS. Use the
down arrow to select Press
ENTER.


Enter
number of favorable outcomes and sample size of samples 1 and 2. Select
the alternate hypothesis. Use down
arrow to select Calculate and press ENTER. 

Results: Since the
p = 0.061, reject the null hypothesis for values of a > 0.061. Conclude that
the sample 1 proportion of 0.305 is significantly greater than sample 2
proportion of 0.24 when a >
0.061. 
