exercise_set_8_fall_2022.pdf - BMGT 230, Exercise Set 8,...

BMGT 230, Exercise Set 8, Due 18 November 2022 (on-line, by 11:59 pm College Park time)
1. L. F. Gilbreth, the vice president of human resources for a major U.S. airline, wants to compare four
programs for training employees to perform a certain task. Twenty employees are randomly assigned to
the training programs, with five in each program. At the end of the training period, the number of times
each employee can perform the task in a five-minutes period is recorded as follows:
PROGRAM 1 PROGRAM 2 PROGRAM 3 PROGRAM 4
9 10 12
12 6 14
14 9 11
11 9 13
13 10 11
L. F. conducts an analysis of variance [ANOVA] test to compare the training programs
a. State the null and alternative hypotheses associated with the test.
b. If SSB = 54.95 and SST = 96.55, what is the calculated value of the associated test statistic?
c. If the level of significance equals 0.05, what is the critical value of the associated test statistic?
d. State your decision regarding the null hypothesis.
e. State your conclusion (meaning, describe what the decision means in this problem).
f. If Tukey’s HSD equals approximately 2.92, which training programs differ significantly from each
other in terms of the number of times employees can perform the task in a five-minutes period, on
average?
2. Hopkins Johns studies college and university students. Recently, Hopkins conducted an analysis of
variance [ANOVA] test to determine whether the amount of time students study per day, on average,
differs, or varies, based on a student’s year in college (first-year, sophomore, junior, senior). To conduct
the test, Hopkins recorded the number of hours studied for eight students selected at random from each
year in college.
a. State the null and alternative hypotheses associated with the test.
b. If the value for SSB equals 16 and the calculated value for the associated test statistic equals
approximately 1.69696969, determine the value for SST.
c. If the level of significance equals 0.05, determine the critical value for the associated test statistic.
d. State your decision about the null hypothesis.
e. State your conclusion (meaning, describe what the decision means in this problem).
9
8
11
7
8

3. A study showed 110 cases of “blue lung disease” among 1,000 instructors who used blue dry erase
markers in classes and 90 cases of “blue lung disease” among 1,000 instructors who did not use blue dry
erase markers in classes. Test whether instructors who used blue dry erase markers in classes were
significantly more likely to develop “blue lung disease” than instructors who did not use blue dry erase
markers in classes.
a. State the null and alternative hypotheses associated with the test.
b. What is the calculated value of the associated test statistic?
c. What is the p-VALUE for the test (please use FOUR decimal places)?
d. If α = 0.05, state your decision regarding the null hypothesis by comparing α to the p-VALUE.
e. State your conclusion (meaning, describe what the decision means in this problem).
4. Recently, the Maryland Gaming Commission has received complaints from numerous patrons of the
Maryland Live! Casino in Hanover, Maryland, regarding the dice game known as Craps. The complaints
generally state that the dice at the casino appear to be “loaded,” meaning unfair. To investigate, you
select a random sample of dice from the casino and test whether each die is fair, meaning whether each
of the six sides is equally likely. The results for one die follow:
VALUE f