Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB

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1 Stats for Strategy Fall 2012 First-Discussion Handout: Stats Using Calculators and MINITAB DIRECTIONS: Welcome! Your TA will help you apply your Calculator and MINITAB to review Business Stats, and will also help you set up Virtual Desktop (for MINITAB) on your computer. Access the Calculator Help website (maintained by Miami University) from the link on the Main Stats Website: blake/econ2800 If your calculator model is listed, follow the directions for Worked-Out Example for Mean and Standard Deviation. If your calculator isn t listed then Google directions for Sample Standard Deviation. Your TA will preview Topic 2 Examples 4 and 5 that we ll cover during lecture this week. (The MINITAB answers correspond to answers we calculate by hand during class.) Use these MINITAB answers together with Notebook answers as a guide for Homework Assignment 1. (You ll need both hand calculations and MINITAB for HW1.) If you brought your laptop today, your TA will help you install Virtual Desktop near the end of today s Discussion so you can work at home instead of in the computer lab. If you don t finish the worksheet during Discussion (or wish to install Virtual Desktop later), come to the first Friday Afternoon Stats Tutor Lab/Help Session (2:30-3:30 in C207) to finish there. The first HW assignment (and quiz) is due next Monday so don t delay! After completing the worksheet you should be able to Enter several numbers into your calculator to produce answers for the sample mean x and sample standard deviation s. 2. Enter several numbers into MINITAB to produce x and s. 3. Use MINITAB to find P -values and confidence intervals for both the population mean µ (a means problem) and the population proportion p (a proportions problem.) 4. Set up Virtual Desktop and successfully access MINITAB on a home computer. (See page 6.) Problem 1 (Calculating standard deviation) (a) Find the instructions in your Calculator Help printout for the worked-out example to calculate x and s for the sample of four numbers Can you get the correct answers? Answers: x = 18 s = (b) Input three numbers into your calculator and calculate x and s: 7, 8, 9 x = s = 1

2 (c) Calculate x and s for this sample (round to 2 decimal places): 4.3, 5.9, 7.0, 4.6, 8.2, 4.4 x = s = (d) Now reproduce your answers with MINITAB. Enter each sample of data into a worksheet column and use the commands Stat > Basic Statistics > Display Descriptive Statistics Do you get the same answers for x and s from MINITAB (except for rounding)? Problem 2 (Apply MINITAB to Topic 2 Example 4) Below is a copy of Topic 2 Example 4 taken from page 40 of the Notes: Your company sells exercise clothing on the Internet. To help design the clothing, you collected the weights (in kilograms) of a sample of six customers: Customer weights are normally distributed. (a) Is it true that the mean weight for all customers is less than 70 kg? Test using the Four Steps and α =.01. (b) Find a 95% confidence interval for the mean weight of all customers. (a) Sometimes there are multiple ways to get an answer in MINITAB. Practice three different ways to get the P -value for Example 4 part (a): (a1) MINITAB can replace t and Z tables when calculating P -values. Calc > Probability Distributions > t > (Select Cumulative probability ) > (Input Degrees of freedom: 5) > (Input constant 4.275) > OK Cumulative Distribution Function Student s t distribution with 5 DF x P(X<=x) What is MINITAB s P -value? (Use all decimal places) 2

3 (a2) Use MINITAB to first calculate x and s, then use the Summarized Data option in the One-Sample t Procedure. (Enter the 6 numbers into column C1. Label the column Weights by typing the label into the cell immediately below C1.) > Stat > Basic Statistics > Display Descriptive Statistics > (Select the column for Variables ) > OK Descriptive Statistics: Weights Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Weights Find x and s from the MINITAB output. Continue with the One-Sample t Procedure: Stat > Basic Statistics > 1-Sample t > (Choose Summarized data and input sample size, mean, standard deviation) > (Check the box Perform hypothesis test and enter the hypothesized value) > Options > (Select Alternative less than) > OK > OK One-Sample T Test of mu = 70 vs < 70 95% Upper N Mean StDev SE Mean Bound T P What is MINITAB s P -value? (a3) Use the Samples in Columns option in the One-Sample t Procedure. Stat > Basic Statistics > 1-Sample t > (Choose Samples in columns. Click inside the box, highlight and select the column of data.) > (Check the box Perform hypothesis test and enter the hypothesized value) > Options > (Select Alternative less than) > OK > OK One-Sample T: Weights Test of mu = 70 vs < 70 95% Upper Variable N Mean StDev SE Mean Bound T P Weights Does this output show the same answer for the P -value? 3

4 (b) A confidence interval is two-sided in the sense that the interval can be wrong by being either too low or too high. To get a 95% confidence interval for µ in MINITAB, choose the two-sided option which corresponds to the alternative hypothesis H A : µ 70 Stat > Basic Statistics > 1-Sample t > (Choose Samples in columns. Click inside the box, highlight and select the column of data) > Options > (Select Alternative not equal) > (Select Confidence level 95.0) > OK > OK One-Sample T: Weights Test of mu = 70 vs not = 70 Variable N Mean StDev SE Mean 95% CI T P Weights (56.31, 66.59) (b1) What is MINITAB s confidence interval? (b2) Why does the P -value double in the latest MINITAB output, compared to the previous MINITAB output? (Answer below.) (c) Now try answering a different question, based on the same sample of six customers: (c1) Find the P -value for testing the alternative hypothesis H A : µ > 70 (c2) Why is the P -value from (c1) so high? Also interpret the P -value below. Problem 3 (Apply MINITAB to Topic 2 Example 5) Below is a copy of Topic 2 Example 5 taken from page 43 of the Notes: Example 5 (Financial goals) Suppose that 70% of last year s UI freshman class agreed with the statement Being well-off financially is an important personal goal. A survey found that 132 out of 200 UI freshmen surveyed this year agree with the statement. (a) Does this year s percentage of UI freshmen who agree that being well-off financially is important differ from last year s percentage? Use Four Steps and α =.05. (b) Find a 95% confidence interval for this year s percentage of UI freshman who agree. (c) Which of the answers (a) or (b) is considered more informative, and why? 4

5 (a) Find the P -value: Stat > Basic Statistics > 1 Proportion > (Choose Summarized data and input number of trials and events ) > Check the box Perform hypothesis test and enter 0.7 for the hypothesized value > Options > (Select Alternative not equal) > (Check the box Use test and interval based on normal distribution ) > OK > OK Test and CI for One Proportion Test of p = 0.7 vs p not = 0.7 Sample X N Sample p 95% CI Z-Value P-Value ( , ) Using the normal approximation. What are the exact Z statistic and P -value from MINITAB? (b) Now use the One-Proportion Procedure to get a 95% confidence interval. What is MINITAB s answer? (Use all available decimal places.) (c) Get a 90% confidence interval. What is the exact MINITAB answer? Notes: (1) Always check the box Use test and interval based on normal distribution for proportions problems since our answers for proportions are based on the bell curve. (2) If you want to get both a P -value and a CI, you ll generally have to run MINITAB twice. But Problem 3 shows an exception: MINITAB gives both answers at once if the alternative hypothesis is not equal to. (See Virtual Desktop instructions next page. See Worksheet Answers on last page.) 5

6 Using MINITAB on Virtual Desktop Blake Whitten Aug. 13, 2012 Introduction This note is for students enrolled in ECON 2800 (Statistics for Strategy) who wish to use MINITAB from a home computer through the university s Virtual Desktop. In case of unexpected difficulty, call the ITS Help Desk at (319) (or take your laptop in person to the Help Desk on the second floor of the Old Capitol Mall.) Setting Up Virtual Desktop Virtual Desktop can be used with either Internet Explorer or Mozilla Firefox web browsers on either a Windows PC or a Mac. You ll probably need to do a one-time install of Citrix Metaframe software on your computer to enable the Virtual Desktop connection. Tip: We recommend that you answer Yes when prompted by Citrix to allowing full access to local drives during installation. (That allows you to save files on your computer s hard drive, if you want to.) Installation instructions are found here: Instructions for PC: Instructions for Mac: Connecting to and Using Virtual Desktop Once set up, go directly to the site and log in with Hawk ID and password: When typing in your own data (i.e., not opening a MINITAB data set) open MINITAB directly from Virtual Desktop. When you do wish to open a MINITAB data set from the course website, use Web Browsers > Firefox > Open Course Website (it may be easiest to google Blake Whitten ) > Go to MINITAB Data Sets page, click the file Saving Your Work If you get stuck while working on MINITAB at home we suggest that you save your work and bring it to office hours or the Stats Lab (on a portable drive) to discuss with a TA or Prof. Whitten. Virtual Desktop will not allow you to save files onto your computer s desktop the way you can in computer labs on campus since the desktop shown on Virtual Desktop is literally the desktop of the (remote) computer on the UI campus which is actually running MINITAB! Instead, save your MINITAB work on your computer s C: drive with these commands: File > Save Project As then nagivate from My Computer to C$ on Client (V:) The following link provides more information and an illustration: 6

7 Worksheet Answers Problem 1 (b) x = 8 s = 1 (c) x = 5.73 s = 1.60 (d) Yes Problem 2 (a) (a1) MINITAB s P -value = (a2) From MINITAB output, x = s = 4.90 MINITAB s P -value = (MINITAB rounds the P -value to 3 decimal places for these data.) (a3) Yes (b) (b1) MINITAB s 95% CI: (56.31, 66.59) kg (Same as Example 4 in Notes, except for rounding.) (b2) The new P -value shades both sides of the bell curve. (c) (c1) P -value= (c2) Since sample mean x = < 70, the sample evidence actually favors the null hypothesis. There is a 99.6% risk of error if the null hypothesis is rejected based on the sample evidence. Problem 3 (a) MINITAB: Z = 1.23 P -value = (Same as Example 5 in Notes except for rounding.) (b) MINITAB 95% CI = ( , )% (c) MINITAB 90% CI = ( , )% 7