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

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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= −

2

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

0.05

α

=

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

0.05

α

=

.

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.

3

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