This module provides a homework of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean. The original module has been revised by R. Bloom; some problems have been omitted.
Some exercises from the original version of this textbook have been removed in this revision of this section: #11,12,14,18-24,26,27. They are available at http://cnx.org/content/m17001/
Some of the statements below refer to the null hypothesis, some to the alternate hypothesis.
State the null hypothesis,
, and the alternative hypothesis,
, in terms of the appropriate parameter (
or
).
-
A
Americans work an average of 34 years before retiring.
-
B
At most 60% of Americans vote in presidential elections.
-
C
The average starting salary for San Jose State University graduates is at least $100,000 per year.
-
D
29% of high school seniors get drunk each month.
-
E
Fewer than 5% of adults ride the bus to work in Los Angeles.
-
F
The average number of cars a person owns in her lifetime is not more than 10.
-
G
About half of Americans prefer to live away from cities, given the choice.
-
H
Europeans have an average paid vacation each year of six weeks.
-
I
The chance of developing breast cancer is under 11% for women.
-
J
Private universities cost, on average, more than $20,000 per year for tuition.
Complete solutions to all parts of this problem are available on the instructor's website for this class.
-
A
;
-
C
;
-
D
;
-
G
;
-
I
;
For (a) - (j) above, state the Type I and Type II errors in complete sentences.
Complete solutions to all parts of this problem are available on the instructor's website for this class.
-
A
Type I error: We believe the average is not 34 years, when it really is 34 years. Type II error: We believe the average is 34 years, when it is not really 34 years.
-
C
Type I error: We believe the average is less than $100,000, when it really is at least $100,000. Type II error: We believe the average is at least $100,000, when it is really less than $100,000.
-
D
Type I error: We believe that the proportion of h.s. seniors who get drunk each month is not 29%, when it really is 29%. Type II error: We believe that 29% of h.s. seniors get drunk each month, when the proportion is really not 29%.
-
I
Type I error: We believe the proportion is less than 11%, when it is really at least 11%. Type II error: WE believe the proportion is at least 11%, when it really is less than 11%.
For (a) - (j) above, in complete sentences:
-
A
State a consequence of committing a Type I error.
-
B
State a consequence of committing a Type II error.
For each of the word problems, use a solution sheet to do the hypothesis test.
If you are using a student-t distribution for a homework problem below, you may assume that the underlying population is normally distributed. (However, in general, a statistician would first need to verify that this assumption is reasonable before applying a t-test.)
