1)An automobile rustproofing company claims that their method protects cars
for an average of 55 months. This hypothesis is tested against the alternative
that the protection lasts for more than 55 months. A random sample of 200 cars
produces an average protection time of 56 months with a standard deviation of 15 months.
Test the hypothesis at the 5% level of significance.
(5)
2) A bank manager wishes to know if the effectiveness of the two manager training
methods he uses is different. Ten management trainees who were taught by method 1,
averaged a score of 86 on a test with standard deviation = 6.
Twelve employees taught by method 2 scored an average of 81
with standard deviation = 4 on the same test.
Conduct a hypothesis test at the 5% level of significance.
(5)
3) A drug company wants to test whether it is really true that 20% of the patients
who take one of their products suffer side effects from the drug.
In a random sample of 150 patients, 42 suffer the side effects.
a) Conduct a 2-tail hypothesis test with a = 0.01.
(4)
b) Conduct a 1-tail hypothesis test with a = 0.01 where Ha is that
the probability of side effects is greater than 20%.
(3)
4) A TV station wants to determine if there is a difference in the proportions of people
who watch 2 of their programs. In random samples of 60 and 80 people,
25 and 40 watched the first and 2nd program respectively.
Conduct the test at the 5% level of significance.
(5)
5) Six junior executives were sent to a class to improve their verbal skills.
To test the quality of the program, they were tested before and after taking
the course, with the following results:
| NAME | BEFORE SCORE | AFTER SCORE |
| Marcia | 18 | 30 |
| Nevin | 38 | 70 |
| Marie-Josée | 8 | 20 |
| Bob | 10 | 4 |
| Steward | 12 | 10 |
| Tammy | 12 | 20 |
Do these results indicate a significant difference in the before and after verbal skills?
Test at the 10% significance level.
(7)
6) A teachers' organization wants to determine if women students spend
more time studying than men students. A sample of 80 women studied an
average of 25 hrs/week with r = 4.5 hrs. A sample of 70 men studied an
average of 23 hrs/week with r = 7.5 hrs.
a) Test the hypothesis using the 1% level of significance.
(4)
b) Find the tail probability or p-value.
(2)
c) Find the value of 
necessary to reject Ho.
(2)
7) A deodorant manufacturer claims that the mean drying time of their product
is at most 15 minutes. A sample of 16 cans yielded a mean drying time of 18 min.
with s = 6 min. Test the claim at the 5% significance level.
(6)
8) A student wants to take a statistics course with a teacher who is a very easy marker.
There are 3 teachers scheduled to teach the course. The student obtains a random
sample of grades given by the 3 teachers in the past.
| Professor | ||||
| Grade | #1 | #2 | #3 | TOTAL |
| A | 10 | 12 | 28 | 50 |
| B | 15 | 30 | 25 | 70 |
| C | 35 | 30 | 15 | 80 |
| TOTAL | 60 | 72 | 68 | 200 |
Using the 1% level of significance, test the hypothesis that a student's grade
was independent of the student's teacher.
(7)
TOTAL (50)
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