Supplemental Instruction Handouts
Statistics
Chapter 10
Two – Sample
Tests of Hypothesis
1.
The purchasing director for an industrial parts factory is investigating the possibility of
purchasing a new type of milling machine. She determines that the new machine will be
bought if there is evidence that the parts produced have a higher average breaking strength
than those from the old machine. The standard deviation of the breaking strength for the
old machine is 10 kilograms and for the new machine is 9 kilograms. A sample of 100 parts
taken from the old machine indicated a sample mean of 65 kilograms, whereas a similar
sample of 100 from the new machine indicated a sample mean of 72 kilograms. Using the
0.01 significance level, is there evidence that the new machine has a higher average breaking
strength than the old machine?
A)
B)
C)
D)
E)
F)
G)
2.
Is this a one or two tail test?
If a one tail test, which tail is it?
State the null and alternative hypothesis.
What is the critical value?
What is the test statistic?
What is your decision?
What is the p-value?
An industrial psychologist wishes to study the effects of motivation on sales in a particular
firm. The psychologist has chosen a sample of 24 new salespeople. She assigned 12 of them
to be paid an hourly rate and the other 12 to be paid a commission. The following data
represents the sales volume (in thousands of dollars) achieved by the first month on the job
of these 24 salespeople.
Hourly Rate
256
212
239
216
222
236
207
219
228
225
241
230
Commission
224
261
254
228
273
234
285
225
237
232
277
245
Is there evidence that wage incentives (through commission) yield greater average sales volume than
those employees who are paid on an hourly basis? (Use the 0.01 significance level)
A) Is this a one or two tail test?
B) If a one tail test, which tail is it?
C) State the null and alternative hypothesis.
D) What is the critical value?
E) What is the test statistic?
F) What your decision?
G) What is the p-value?
Learning Assistance Centre
www.rrc.mb.ca/lac
These questions are compiled by Mike Reimer for the Learning Assistance Centre.
3.
Recently, some engineering students decided to test nine cars that normally use regular
gasoline. The test was conducted to see what would happen to those cars if they were filled
with high – octane gasoline. The cars were driven under similar road surface, weather and
other driving conditions. The chart below shows the engineering students’ results for each
of the nine cars and the mileage driven for each gasoline type:
Car
Gas Type
1 2 3 4 5 6 7 8 9
Regular
15 23 21 35 42 28 19 32 31
High-Octane 18 21 25 34 47 30 19 27 34
According to this data, does regular gasoline give you less miles per gallon than high - octane
gasoline? (Use the 0.05 significance level)
A)
B)
C)
D)
E)
F)
G)
4.
Is this a one or two tail test?
If a one tail test, which tail is it?
State the null and alternative hypothesis.
What is the critical value?
What is the test statistic?
What is your decision?
What is the p-value?
A professor of accountancy was studying the readability of the annual reports of two major
companies. A random sample of 100 certified public accountants was selected. Fifty were
randomly assigned to read the annual report of company A, and the other fifty were to read
the annual report of company B. On the basis of a standard measure of readability, 17 found
company A’s annual report “understandable” and 23 found company B’s annual report
“understandable.” At the 0.05 significance level, is there evidence of a significant difference
between the two companies in the proportion of CPA’s who find the annual reports
understandable?
A)
B)
C)
D)
E)
F)
G)
Is this a one or two tail test?
If a one tail test, which tail is it?
State the null and alternative hypothesis.
What is the critical value?
What is the test statistics?
What is your decision?
What is the p-value?
Learning Assistance Centre
www.rrc.mb.ca/lac
These questions are compiled by Mike Reimer for the Learning Assistance Centre.