STAT 121: Writing Assignment 2- Significance Test and Confidence Interval

| August 30, 2017

Question
STAT 121: Wri+ng Assignment 2
Significance Test and Confidence Interval (24 points)
Direc+ons: Read the following problem, and follow direc5ons, and answer each ques5on completely but
concisely. Be sure to save a copy of your work, and see the syllabus for submission details. (The spacing
between the ques5ons is not necessarily an indica5on of the expected response length.)
The Situa+on
The manager of a large manufacturing company claims that the mean income for all his senior assemblyline
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:
495 470 475 480 485 500 465 475
490 495 505 510 485 490 460 490
You may use any sta,s,cal so/ware to answer the following ques,ons.
Part A. Test of Significance
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-pairs t-test for
means). (1 pt)
2. Describe the parameter of interest in the context of the problem. (1 pt)
3. State the null and alterna5ve 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. List and check the condi5ons for the test procedure you named above. (4 pts)
7. Use CrunchIt!, Excel, or a graphing calculator to get the values of the sample mean and sample
standard devia5on. (1 pt)
8. State the test sta5s5c value (including your calcula5ons) and the associated P-value using the
appropriate table, not from sta5s5cal soYware. (2 pts)
CONCLUDE:
9. Answer the ques5on posed in the STATE step in context. Do this by including these three parts in
your conclusion (3 pts):
• Compare P-value with ?.
• Decide whether to reject or fail to reject the null hypothesis (“reject H?
” or “fail to reject H?
”).
• State your conclusion in context.
Part B. Confidence Interval Es+ma+on
STATE:
What is a 95% confidence interval es5mate of the mean weekly salary of all senior assembly-line workers
in this manufacturing company?
PLAN:
1. State the name of the appropriate es5ma5on procedure (e.g. matched-pairs t-confidence
interval for es5ma5ng the mean difference). (1 pt) (Note: You have already described the parameter
being es,mated in part A, so you don’t have to repeat it here.)
2. State the confidence level. (1 pt)
SOLVE:
(Note: You have already ploIed the data and checked the condi,ons in part A, so you don’t have to redo
it here.)
3. Restate the values of the sample mean and sample standard devia5on. (1 pt)
4. Write down the t* cri5cal 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 es5mate

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