MTH 380 Lecture Notes - Lecture 10: Air1, Paired Difference Test, Test Statistic

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22 Nov 2020
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ASSIGNMENT 10, Test of hypotheses
Part 1
Chapter 9, Large - Sample test of hypothesis.
Ch.9.2. A large - sample test about population mean
1. Ch.9.2, 6, 7, 8, 9, p.352 (modified)
Find the appropriate rejection region for large - sample test of hypothesis about population
mean based on standard normal variable.
a. A right -tailed test with
0.01
α
=
;
b. A left -tailed test with
0.01
α
=
;
c. A two -tailed test with
0.01
α
=
;
d. A right -tailed test with
0.05
α
=
;
e. A left -tailed test with
0.05
α
=
;
f. A two -tailed test with
0.05
α
=
;
6. Observed value of test statistic was z = 2.16
For a right tailed with
0.01
α
=
state whether null hypothesis is rejected or not
rejected.
7. Observed value of test statistic was z = 2.16
For a two tailed with
0.05
α
=
state whether null hypothesis is rejected or not
rejected.
8. Observed value of test statistic was z = - 2.41
For a left tailed with
0.01
α
=
state whether null hypothesis is rejected or not
rejected.
9. Observed value of test statistic was z = - 2.41
For a two tailed with
0.01
α
=
state whether null hypothesis is rejected, or not
rejected.
2.Ch.9.2, 11, 12, 13, p.352
Find p values for the following large - sample z tests.
Using found p values decide whether null hypothesis should be rejected or not, and
determine the significance of results.
a. A right tailed test with
.
1.15
obs
z=
.
b. A two tailed test with
.2.78
obs
z=
c. A left tailed test with
.1.81
obs
z=
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3. Ch. 9.2, 14, 15, 16, 17, p.352 (modified and combined into one problem)
A random sample of n = 35 observations from quantitative population produced a mean
x
= 2.4 and a standard deviation s = 0.29.
Suppose your research objective is to show that the population mean exceeds 2.3.
a. Use critical value approach to test the hypothesis. Assume
b. Calculate the p value for the test and use it to draw a conclusion about rejection of
null hypothesis at 5% significance level.
Assume predetermined level of significance is
0.05
α
=
4. Ch.9.2, 21, p.352
A random sample of n = 100 observations from quantitative population produced a mean
x
= 26.8 and a standard deviation s = 6.5.
a. Use the critical value approach to determine whether population mean is different
from 28. Assume
0.05
α
=
.
b. Use p value approach to determine whether population mean is different from 28.
Assume predetermined level of significance is
0.05
α
=
5. Example 9.5, p.343 & Example 9.6, p.345
The quality control manager wants to know whether the daily yield at a local chemical plant
which has averaged 880 tons for the last several years has changed in recent months.
A random sample for n= 50 days gives an average yield of 871 tons. Sample standard deviation
is 21 tons. Is there a sufficient sample evidence to indicate that mean yield has changed?
9.5. Use critical value approach to test the hypothesis. Assume
.
9.6. Use p-value approach to solve this problem.
Assume predetermined level of significance is
0.05
α
=
6. Example 9.8, p. 349 optional, not for the test
The quality control manager wants to know whether the daily yield at a local chemical plant
which has averaged 880 tons for the last several years has changed in recent months.
A random sample for n= 50 days gives an average yield of 871 tons. Sample standard deviation
is 21 tons. Calculate
β
and the power of the test
1
β
when actual value of the test is 870
tons.
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7. Example 9.7, p.346
Standards set by governmental agencies indicate that Canadians should not exceed an average
daily sodium intake of 3300 mg. To find out whether Canadians are exceeding this limit, a
sample of 100 Canadians is selected, and the mean and standard deviation of daily sodium
intake are found to be 3400 mg and 1100 mg respectively.
Use
0.05
α
=
to conduct the test of appropriate hypothesis using critical approach and p
value approach.
8. Ch. 9.2, 22, p.352
9. Ch.9.2, 23, p.352
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