How to construct a confidence interval in minitab

Homework

There are 4 sets of homework, one set for each block. Some problems in the homework require using Minitab program and data files. Minitab program is installed on all the PCs on SCSU campus. Off campus, users can access Minitab program through APPS ANYWHERE (virtual lab), contact Technology Help at SCSU E-mail: huskytech@stcloudstate.edu; Phone: (320) 308-7000 for assistance.

All the data files for Minitab program are posted on the D2L in Minitab Data for Homework module. Download the Minitab data files on your USB (or a PC with Minitab program installed). Please read MINITAB GUIDE in the pages 13-14 in the text book to get familiar with starting Minitab, entering data, opening worksheet and etc. For a problem that is required to use Minitab, note the Minitab Guide reference.

All your homework is due at the period in the schedule by submitting in the submission box on D2L. On your syllabus, the due date for individual blocks are indicated as well as on the corresponding submission box. The submission box will be closed after the due date.

Late homework should be submitted by email within 5 days from the due date; homework submitted late without permission in advance or without a legitimate reason will be subject to a 50% penalty. Homework submitted late but with permission in advance or legitimate reason will be subjected to a penalty rate of my discretion. NO homework for any blocks will be accepted after five days from the due date or the last day of class.

I prefer to have the homework submitted in word format. Use copy and paste to include Minitab outputs and graphs in the Word file to submit. Submit all questions in each block in one packet with clear identification information such as homework number, the name of the student, course number.

Block 1 Homework Problems (30 pts):

1.1 Describe the differences with one example each between descriptive statistics and inferential statistics(5 pts)

1.2 Describe the differences with one example each between statistic and parameter (5 pts).

1.3 The following data is I-94 exit numbers. What level of measurement is it and why? (5 pts)

258 – Lakeland, St Paul; 215 – Plymouth; 193 – Monticello;

183 – Maple Lake; 178 - Clear Lake; 171 -- St Cloud; 164 – St. Joe;

100 – Alexandria; 6 -- Moorhead Airport

1.4 For the Retirement Funds.MTW file, compute descriptive statistics of 1YrReturn% and create boxplots of 1YrReturn% in various types (growth and value) (5 pts)

To get the Minitab output:

To open Retirement Funds file in a PC with Minitab installed:

Select .File Open Worksheet, select the data file (Retirement funds) click OPEN and OK

Go to topline menu – click Stat Basic statistics Display Descriptive Statistics

In the dialog box, double click the name of the column containing data (1YrReturn%) in the left column.

In the dialogue box, click OK or Statistics to check statistic you want

The session window shows output (results), Select (mark) results, copy and paste on Word file to submit.

Or by following the step by Minitab Guide in pp. 164-165 (MG1 and MG3)

To get Boxplots:

With the Retirement funds file open,

Select Graph boxplot

Choose one Y with group > OK

Double click 1YrReturn% in the variable list

Click categorical variable box and double click Type in the variable list to add type in Categorical variables box

Click OK

Right click on the Boxplot, copy graph and paste on the Word file.

1.5 Do problem 61 in page 202 (5 pts)

1.6 Do problems 3 and 5 in page 262 by showing all steps (5 pts)

Block 2 Homework Problems (40 pts):

2.1 Describe the three properties of sampling distribution of sample mean (6 pts)

2.2 Do problem 1 in page 295 (4 pts)

2.3 Do problems 1 and 2 in page 316, problem 11 on page 323 and problems 34 and 35 in page 332 (4 pts)

2.4 Do problems 11 (H0 : the drug is unsafe, H1 : the drug is safe), and 13 in page 363

(6 pts)

2.5 Confidence intervals; use MINITAB for the FORCE data file which is in the Minitab Data for Homework, construct confidence intervals of the population mean force (90%, 95%, and 99%) using t-distribution (10 pts).

To get the Minitab output:

To open Force file in a PC with Minitab installed:

Select .File Open Worksheet, select the data file (Force) click open and OK

Go to top line menu – click Stat Basic statistics 1t – 1 Sample t

In the dialog box, click Samples in columns box, and double click Force in the left column.

Click Options in the dialogue box (1-Sample t – Options), enter 90.0 in the Confidence level Box.

Click Ok and Ok.

Go to topline menu and repeat for confidence level 95.0 and 99.0

The session window shows output (results), Select (mark) results, copy and paste on Word file to submit.

2. 6. Hypothesis tests --Use Minitab, answer problem 30, part a) on page 368, use both t and p-Value for DRINK file. Submit Minitab output with Hypothesis test using t and showing all 6 steps as in pages 364-5 (to simplify combine steps 3 and 4 together, then the six step approach becomes five step approach which is more common) and p-Value (5 steps as in page 366). Test the hypothesis using the t and p-Value both following 5 steps below (10 pts)

To get the Minitab output:

To open Drink file in a PC with Minitab installed:

Select .File Open Worksheet, select the data file (Drink) click open and OK

Go to topline menu – click Stat Basic statistics –> 1t – 1 Sample t

In the dialog box, click Samples in columns box, and double click Fill in the left column to enter the name of the column Fill to Samples in columns box (or simply type in Fill Samples in columns box)

Check Perform hypothesis test, type 2 in the Hypothesized mean box

Click Ok

You will get the following output

Use the T and p for hypothesis test f by following the steps

--------------------

Welcome to Minitab, press F1 for help.

Results for: DRINK.MTW

One-Sample T: Fill

Test of mu = 2 vs not = 2

Variable N Mean StDev SE Mean 95% CI T P

Fill 50 2.00072 0.04456 0.00630 (1.98806, 2.01338) 0.11 0.910

--------------------------

Or Refer MG2 in page 387, follow the un-summarized data steps and in step 3 check perform hypothesis test and enter 2 in the hypothesized mean box, and Click OK.

5 steps using t or z (as a test statistic and It is 5 step critical value approach) are:

1. State H0 and H1

2. Determine the level of significance of test: α such as 0.01. 0.05 or 0.1

3. Set-up critical value(s) – this means determining what test statistic to use and rejection area(s) – this step is a combination of steps 3 and 4 in the 6 step Critical value approach in page 364 of text. {For p-value, reject H0 if p-value < α}

4. Calculate the test statistic (use t = 0.11 from above Minitab output)

5. Make inference – conclusion

5 steps using p-Value (as a test statistic) are:

1. State H0 and H1

2. Determine the level of significance of test: α such as 0.01. 0.05 or 0.1

3. Set-up critical value(s): reject H0 if p-value < α

4. Calculate the test statistic (use p-value = 0.910 from above Minitab output)

5. Make inference – conclusion

Block 3 Homework Problems (30 pts):

3.1 χ 2 - Test of Independence (15 pts)

Perform 5 step Hypothesis tests {H0 : Hotels and reason for not returning are independent -not related vs. H1: Hotels and reasons are not independent – related} using α = 0.05 and Minitab output.

To get the Minitab output (refer Figure 10 page 411 too), click File -> Open Worksheet and select open PalmHotels data file to the worksheet; select Stat -> Tables -> χ 2 Test (two-way table in worksheet), In the χ 2 - Test dialog box, enter the names of column C1 to C3 in the columns containing the table by double clicking variable name in the left column, and click Ok. Minitab generates output on the session window>

Refer the Minitab output on the right side of Figure 10 page 411 in textbook

From the Minitab output, use the χ 2 (Chi-sq) and p-Value to perform 5 step hypothesis tests and submit Minitab output with Hypothesis tests using X2 and p-value, use α = 0.05.

Please refer the steps for hypothesis test using χ 2 and p-Value in the Summary for Block 3 file in Summary & Formulas Module posted on D2L.

3.2 Regression outputs (5 pts).

Use MINITAB, get regression output of Table 1 in page 444 (use SiteSelection data file). Annual Sales is y (Response), and Profiled Customers (both in millions) is x (Predictors). Also, predict Annual Sales when the Profiled Customers is 4.

To get Minitab output,: After opening Minitab, File -> Open Worksheet by selecting SiteSelection , clicking open and OK (the PC should have Minitab installed), select Stat Regression Regression. In the dialogue box, double click Annual Sales, and double click Profiled Customers. Click Options and enter 4 in the Prediction Interval for new observations, and Ok and OK.

The session window shows output (results), Select (mark) results, copy and paste on Word file to submit.

(Or follow steps 1, 2, 10, 13,15 and 16 to get Minitab. refer MG2 in page 491)

Your submission includes a) complete Minitab output b) regression equation, r2, predicted sales for Profiled customer is 4 c) Hypothesis test on slope β 1 using t and p with α = 0.01

Please refer the steps for hypothesis test using t and p-Value in the Summary for Block 3 file in Summary & Formulas Module posted on D2L.

Refer the example in Summary for Block 3 file in Summary & Formulas Module posted on D2L

3.3 Table 1 on page 498, use OMNIPower data file and Minitab, get regression output. Predict sales at price =79 and promotion = 400 (5pts).

To get Minitab output,: After opening Minitab, File -> Open Worksheet by selecting OMNIPower, clicking open and OK (the PC should have Minitab installed), select Stat Regression Regression. In the dialogue box, double click Sales, and double click Price , promotion ( sales is in the response box, and price promotion are in the Predictors box). Click Options and enter 79 400 in the Prediction Interval for new observations, and Ok and OK.

The session window shows output (results), Select (mark) results, copy and paste on Word file to submit.

Or refer the MG1 in page 547 (not 546): After opening to the OMNIPower worksheet, select Stat Regression Regression. Follow steps 1, 2, 3, 13, 16(enter 79 and 400 in the Prediction interval for new observations), and 18 (OK). (The second predictor promotional Expenses is the same with Promotion)

Submit Minitab output and perform a Hypothesis test for the significance of the overall model by F and p-value, use α = 0.01.

Please refer the Steps for hypothesis test using F and p-Value in the Summary for Block 3 file in Summary & Formulas Module posted on D2L Here are formats (Complete all steps)

3.4 Indicator variable (5pts)

Use MINITAB to get regression outputs of SilverSpring data file.

After opening Minitab, File -> Open Worksheet by selecting SilverSpring, clicking open and OK (the PC should have Minitab installed), select Stat Regression Regression. In the dialogue box, double click Asking Price, and double click Size, Fireplace Coded ( Asking Price is in the response box, and Size, Fireplace Coded are in the Predictors box). Click Options and O.

The session window shows output (results), Select (mark) results, copy and paste on Word file to submit.

Fireplace Coded in column C11 is an indicator variable. Fireplace Coded is generated by assigning/putting 0 for no Fireplace and 1 for Fireplace in the Fireplace column C10-T.

Since it is a multiple regression, follow the same steps explained in problem 3.3 but skip options.

Submit Minitab output.

Block 4 Homework Problems (40 pts):

4.1 Use MINITAB, construct X-bar chart and R chart for the data in Hotel2 file (10 pts). Interpret the results (Interpretations are in the session window).

Refer MG5 on page 637. After opening Minitab, File -> Open Worksheet, select Hotel2, click open and OK. (The PC should have Minitab installed). Select Stat Control Charts Variable chart for Subgroups R chart, In the dialogue box, top of right-side, select Observations for a subgroup are in one row of column, Click the box below, double click Time 1 Time 2 Time 3 Time 4 Time 5 , next click R-Options, in the R-option dialog box, click test tab and choose to Perform all tests for special causes from the drop-down list; click S limits tab and enter 1 2 3, there is a space between numbers 1 2 and 3, OK, and OK

To enter variables (Time 1 to Time 5) by double clicking each variable or c2-c6, if you don’t see the variable list, click right-hand side box. S limits command subdivides the control chart into zone A, B, and C.

After R-chart, do X-bar chart always (replace R by X-bar and follow the above steps)

Copy control chart and session window, paste on a Word file to submit

4.2 Construct p-chart for the data in ERRORSPC file (5 pts). Interpret the result

To get Minitab output:

Open ERRORSPC file. Select Stat Control Charts Attributes Charts P.

In the P-chart dialog box, enter Nonconfm in variable box by double-click c1 Nonconfm in the variable list, enter 200 in the subgroup size box, and click p-chart options box,

In P-chart Options, click Tests tab and choose to Perform all tests for special causes from the drop-down list, and click S limits tab, enter 1 2 3, OK, and OK.

(Refer MG2 on page 636(it is explained using Hotel1 data file, and applied the first two tests, apply all test)

Copy control chart and session window, paste on a Word file to submit

4.3 Construct c-chart for the data in COMPLAINTS file (5 pts). Interpret the result

To get Minitab output:

Open COMPLAINTS file and select Stat Control Charts Attributes Charts C.

in the c-chart dialog box, enter Complaints in variable box by double-click c1 Complaints in the variable list. In c-chart options box, click Tests tab and choose to Perform all tests for special causes from the drop-down list, and click S limits tab enter 1 2 3, OK and OK (or Refer MG4 in pages 636-7)

Copy control chart and session window, paste on a Word file to submit

Only X-bar chart apply 8 tests and all others (P, C and R-charts) apply the first 4 tests.

Refer the list of tests in the References Module in D2L content

4.4 Do problem 3 parts c (construct payoff table) and e (converting payoff table to opportunity table) in page 671 (10 pts)

Converting the payoff table to opportunity loss (OL) table

Refer Table 3 or Table 4 in pages 670-1 of textbook

For the Payoff table (Table 3);

A1: Gradual

A2 Concentrated

E1: low demand

1

-5

E2: High demand

4

10

You may think this way to get opportunity loss table:

· if in Low demand, E1, you will choose gradual alternative and profit is 1, OL of gradual action is 0, but OL of the Concentrated alternative is 6, because you lose 5, in fact, you could make 1, so the amount of regret(OL) is 6

OL = largest payoff in the line (event) – the payoff of the cell

· If in High demand, E2, you will choose Concentrated, OL is 0, for Gradual OL= 10 -4 = 6

Key is to think in one event i.e. low demand at a time and move to next event i.e. high demand

The Opportunity Loss table is:

A1: Gradual

A2 Concentrated

E1: low demand

0

6 (1-(-5))

E2: High demand

6 (10- 4)

0

4.5 Do problem 7 in page 679 (10 pts) Refer examples in pp 672-679

End