STAT177 homework sheet #5
A microchip manufacturer embarked on a quality control program to see
if the percentage of scrap microchips could be reduced to less than 1.2%. Six
months after the program, an hour’s production was chosen as a sample. Out of
562 chips produced, 5 were scrap.
1)
State the null and
alternative hypotheses. (set up as a left tail test)
2)
Based on the results,
were the quality control measures effective? Test at 5%. (p-value = 0.25;
conclude the measures were not effective)
3)
What type of error
could have been committed? (Type II)
4)
Suppose they had
initially chosen a level of significance of 10%. Would the verdict have
changed? (no, since the p-value would still be greater than the level of
significance)
A store wanted customers to fill out its new online survey. When
customers paid for their purchases, the clerk would point out the website
address on the receipt. The store would consider this method of marketing the
survey successful if the percentage who actually did the survey was greater than
1 in 800. For a particular weekend, the store had 2,538 customers of which 8
did the online survey. Test at 5%.
5)
State the null and
alternative hypotheses. (set up as a right tail test)
6)
What is the
appropriate test for this situation and why? (exact binomial test since the
number of expected successes < 5)
7)
Based on the results,
is the marketing method successful? (p-value = 0.016; conclude the marketing
method is successful)
8)
Suppose a level of
significance had not been chosen. Why would the same conclusion be reached?
(p-value of 0.016 provide good support for Ha)
In small rural school, it is common to have elementary through high
school under one roof. One such small rural school was guinea-pigged for a
project to see if the percentage of students who achieved the acceptable grade
on provincial exams would change from the current percentage of 78%. There were
42 students from grades 3, 6, 9 and 12 who wrote the test of which 35 achieved
the acceptable grade.
9)
State the null and
alternative hypotheses. (set up as two-tail test)
10) What is the appropriate test for this situation? (Z
test)
11) Based on the results, is there any significant
change in the percentage of students who achieve the acceptable grade on the
exam? (p-value = 0.404; conclude no significant change)
12) Based on the 95% confidence interval, what is the
maximum percentage of students who achieve an acceptable grade on provincial
exams? (94.6%)
In a market research phone room, it is easier to predict how long it
will take to complete the field work if the average completion rate per hour is
consistent. They like to maintain a standard deviation of under 1 survey per
hour for a 6-hour shift. For one shift with 15 interviewers, these were the
average completion rates per hour:
|
2.7 |
2 |
3.5 |
2.9 |
3.4 |
|
2.1 |
2.4 |
3.9 |
1.9 |
3 |
|
2.5 |
1.2 |
3.2 |
2.6 |
2.7 |
13) What is the null and alternative hypotheses (set up
as a left-tail test)
14) Were the standards being maintained for this shift?
Test at a 5% level of significance. (p-value = 0.058; conclude the standard
deviation is not low enough)
15) Is there a level of significance between 1% and 10%
in which the opposite conclusion would have been reached? (between 5.8% and
10%)
From the text, read:
Chapter 4, pages 64-76