Stat 1000: Assignment 5 Tips (Classroom Lecture Sections)

Published: Wed, 11/21/12

My revised tips for Assignment 5 are coming below, but first a couple of announcements.

Please note that my final exam prep seminar for Stat 1000 will be on Saturday, Dec. 1, in room 100 St. Paul's College, from 9 am to 9 pm . Do note that this seminar tends to fill up, so to ensure admittance, make sure you register in advance. For complete info about the seminar, and to register if you have not done so already, click this link:

Stat 1000 Seminar

I am also offering seminars in Calculus, Linear Algebra, and Stat 2000 in the coming weeks. You can get info about those seminars here:

Grant's One-Day Exam Prep Seminars

If you ever want to look back over a previous tip I have sent, do note that all my tips can be found in my archive. Click this link to go straight to my archive:

Grant's Homework Help Archive

Make sure you have read my Tips on How to Do Well in this Course

Did you miss my Tips on what kind of calculator you should get? Click here

Did you miss my Tips for Assignment 4? Click here

If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 11.

Tips for Assignment 5 (Classroom Lecture Sections A01, A02, A03, etc.)

Study Lesson 8: Confidence Intervals for the Mean and Lesson 9: Hypothesis Testing for the Mean in my book, if you have it, to prepare for this topic.

You will be using Table A and Table D while learning Lesson 8 and 9 and doing this assignment. Here is a link where you can download those tables if you have not done so already:

Table A

Table D

First, be sure to note whether a question gives you σ, the population standard deviation, or s, the sample standard deviation. That dictates whether you will use z or t when making your confidence interval or testing your hypothesis.

Question 1 is using the sample size formula introduced before question 6 in my Lesson 8. Be sure to look at questions 6, 7 and 8 in my Lesson 8 before attempting this question. Be careful in part (f). You may want to take a look at my question 2 in Lesson 7 as an illustration of the concept they are discussing.

Question 2 is standard confidence interval for the mean stuff. Make sure you properly interpret the confidence interval. Look at my question 1(b) in Lesson 8 for an example of that. Also take a look at question 10 in the same lesson for an example of how to deal with an unusual level of confidence.

Question 3 requires some challenging algebra. Take a look at my question 13(c) in Lesson 9 as a starting point for this question.

Step 1: Establish the width of the confidence interval by finding the difference between the upper and lower limit of the confidence interval you are given. Divide the width by 2 and you now know m, the margin of error.

Step 2: You are also given sigma and n, so you can compute sigma(x-bar), the standard deviation of the sample mean (sigma divide by the square root of n).

Step 3: Since the margin of error, m, is z* multiplied by the standard deviation of x-bar, you can simply divide m by the standard deviation to find z*. Put another way, you can take the answer in Step 1 and divide it by the answer in Step 2 to compute z*.

Step 4: If your answer for z* is on Table D, excellent! You can now read off the level of confidence. If your answer for z* is not on Table D, remember that the level of confidence is the area between z* and -z* on the bell curve, so you can figure out that percentage from Table A. Make sure you express the area as a percentage.

Question 4 is good practise at all five steps to test a hypothesis. Make sure you have studied Lesson 9 up to the end of question 12 at least before attempting this question.

Question 5 is much like question 4. Be sure to read the section in Lesson 8 about "Inferences for the Mean are robust" that I write in the pages leading up to question 1 to understand what they are getting at in part (a) (or remind yourself about the Central Limit Theorem in Lesson 7).

Question 6 is yet another runthrough of hypothesis testing. Make sure you look at my Lesson 9, question 13(d) for an example of the concept of using confidence intervals to test hypotheses.

To use JMP, click "New Data Table", then enter the data into Column 1. Double-click Column 1 and name it something appropriate, like "Fill Pressure". Now select "Analyze", "Distribution" and highlight "Fill Pressure" and click "Y, Columns", then click OK. You are now looking at a histogram and stuff.

To test the hypothesis. Click the red triangle next to "Fill Pressure" then select "Test Mean" from the drop-down list. Enter in the mean from your null hypothesis and enter in the given standard deviation . Click "OK" and JMP gives you the hypothesis test at the bottom of the printout. Note that you cannot enter the level of significance they have given. Note that:

Prob > |z| is the P-value for a two-tailed test.

Prob > z is the P-value for an upper-tailed test.

Prob < z is the P-value for a lower-tailed test

JMP gives you the P-values, and you make your decision from that. As they say, you will write out the hypotheses, list the test statistic as given by JMP, list the P-value as given by JMP, and then write your conclusion.

To make the confidence interval. I am not sure if they mean for you to do the confidence interval by hand, or with JMP, but here is how to do it with JMP if you want to check your answer at least. Click the red triangle next to "Fill Pressure" then select "Confidence Interval" from the drop-down list. Select "Other" to get a pop-up menu. It probably already has 0.95 typed in (for 95% confidence interval), but, if not, be sure to type in 0.95. Make sure you click the box saying "Use known Sigma". Click "OK" and you will then get a pop-up menu to type in the sigma value. Click "OK" and JMP gives you the Confidence Interval at the bottom of the printout.

You can now select "File" in the JMP toolbar, and select "Save As" and save the printout as a PDF file and upload it into the HTML editor. Type in the other answers they require and submit.