Posted: May 30th, 2024

STAT 121: Writing Assignment 2 Significance Test and Confidence Interval

STAT 121: Writing Assignment 2
Significance Test and Confidence Interval (24 points)

Directions: Read the following problem, and follow directions, and answer each
question completely but concisely. Be sure to save a copy of your work, and see
the syllabus for submission details.
(The spacing between the questions is not necessarily an indication of
the expected response length.)

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The Problem
The manager of a
large manufacturing company claims that the mean income for all his senior
assembly-line workers is $500 per week. The workers believe that the mean wage
is actually less than $500 and decide to test their manager's claim. A random
sample of 16 workers had the following weekly incomes:

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You may use any statistical software to
answer the following questions. (Note:.byu.edu/statcrunch/index.html">http://statistics.byu.edu/statcrunch/index.html
can be used for this problem [Passcode: BYUStat].)

Part A. Test of Significance

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STATE:
At the ? = 0.05 level, is there sufficient evidence to
conclude that the mean weekly salary of all senior assembly-line workers is
less than $500 per week?

PLAN:
1.
State the name of the
appropriate test procedure you will use (e.g., matched-pairst-test for means). (1 pt)
2. Describe the parameter of interest in the
context of the problem. (1 pt)
3. State the null and alternative hypotheses.
(2 pts)
4. State level of significance. (1 pt)

SOLVE:
5.
Include a plot of the data. Comment
on whether it has one peak and whether there are outliers. (1 pt)
6.
Listand check the conditions for the test procedure you named
above. (4 pts)
7. UseStatCrunch
to get the values of the sample mean and sample standard deviation. (1 pt)
8. State the test statistic value (including
your calculations) and the associatedP-value
using the appropriate table, not from statistical software. (2 pts)

CONCLUDE:
9.
Answer the question posed in
theSTATE step in context.
Do this by including these three parts in your conclusion (3 pts):
•
CompareP-value with ?.
•
Decide whether to “rejectH0” or “fail to rejectH0.”
•
State your conclusion in
context.

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Part B. Confidence Interval Estimation
STATE:
What is a 95% confidence interval estimate
of the mean weekly salary of all senior assembly-line workers in this
manufacturing company?
PLAN:
1.
State the name of the
appropriate estimation procedure (e.g. matched-pairst-confidence interval for estimating the mean difference). (1 pt) (Note:
You have already described the parameter being estimated in part A, so you
don't have to repeat it here.)
2.
State the confidence level. (1
pt)
SOLVE:
(Note:
You have already plotted the data and
checked the conditions in part A, so you don't have to redo it here.)
3.
Restate the values of the
sample mean and sample standard deviation. (1 pt)
4.
Write down thet* critical value. Calculate and record
the confidence interval in interval form. Be sure to show your work. (2 pts)
CONCLUDE:
5.
Interpret your confidence
interval in context. Do this by including these three parts in your conclusion
(3 pts):
•
Level of confidence
•
Parameter of interest in
context
•
The interval estimate

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