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

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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

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

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