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MGMT 6 Summer 2020 Week 11 Homework Questions /202
50
(Last updated 7/8
20)
Chi Square
| Saeko has a yarn shop and wants to test her theory on what types of colors she is selling. | |||||||||||||||||
| She believes that | Black | White | Primary Colors | ||||||||||||||
| The primary colors are blue, red, and yellow; while the tertiary colors are | Brown | Green | Purple | ||||||||||||||
| Test Saeko’s theory using the 5 step hypothesis testing analysis and Chi Square at the .10 level of significance. | |||||||||||||||||
| Here is a pivot table that shows Saeko the number of yards that were sold in the various yarn types during the busiest weekend of her shop last year. | |||||||||||||||||
| Row Labels | Count of | Color Type | Sum of | Y | |||||||||||||
| 23 | 35 | 856 | |||||||||||||||
| Blue | 16 | 17 | |||||||||||||||
| 13 | 1 | 34 | 26 | ||||||||||||||
| 12 | 12509 | ||||||||||||||||
| 12131 | |||||||||||||||||
| Red | 8 | 39 | |||||||||||||||
| 37666 | |||||||||||||||||
| Yellow | 1 | 28 | |||||||||||||||
| (blank) | |||||||||||||||||
| Grand | Total | 1 | 22 | 149908 | |||||||||||||
| 1) | Using the pivot table, fill in the blanks in the following table: | ||||||||||||||||
| Primary Colors consists of the sum of Blue, Red, and Yellow yarn sold | |||||||||||||||||
| Tertiary Colors | |||||||||||||||||
| The Total in this chart must equal the Grand Total, Cell D | 19 | ||||||||||||||||
| This table represents the observed data in the Chi Square analysis. | |||||||||||||||||
| Find the Expected values for each of the colors. Saeko expects that the colors sell in equal amounts. | |||||||||||||||||
| Subtract the Expected values from the observed values | |||||||||||||||||
| Square the values just found | |||||||||||||||||
| Divide each square by the expected value and add together | |||||||||||||||||
| 2) | This total is your Chi Square test statistic | ||||||||||||||||
| Use the 5 step hypothesis testing procedure to determine if Saeko’s hypothesis that the colors sell in equal amounts is true. | |||||||||||||||||
| What is the null hypothesis? | |||||||||||||||||
| What is the alternative hypothesis? | |||||||||||||||||
| What is the level of significance? | |||||||||||||||||
| 3) | What is the Chi Square test statistic? | ||||||||||||||||
| 4) | What is the Chi Square critical Value? | Use =CHISQ.INV() | |||||||||||||||
| What is your answer to Saeko? | State both the statstical answer (reject or do not reject, and what hypothesis), and also state your answer in English: What can Saeko learn from the data? |
ANOVA
| Saeko owns a yarn shop and want to expands her color selection. | |||
| Before she expands her colors, she wants to find out if her customers prefer one brand | |||
| over another brand. Specifically, she is interested in three different types of bison yarn. | |||
| As an experiment, she randomly selected 21 different days and recorded the sales of each brand. | |||
| At the .10 significance level, can she conclude that there is a difference in preference between the brands? | |||
| Misa’s Bison | Yak-et-ty-Yaks | Buffalo Yarns | |
| 799 | 776 | ||
| 784 | 6 | 40 | 931 |
| 807 | 822 | 794 | |
| 675 | 920 | ||
| 795 | 616 | 731 | |
| 875 | 893 | 837 | |
| 4,735.00 | 4, | 60 | 5,012.00 |
| 5) | |||
| 6) | Use Tools – Data Analysis – ANOVA:Single Factor | ||
| to find the F statistic: | |||
| 7) | From the ANOVA output: What is the F value? | ||
| 8) | What is the F critical value? | ||
| 9) | What is your decision? | ||
| Explain in statistical terms |
Regression
| Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per year?” | |||
| Age ( | X | Time (Y) | |
| 123,556.00 | |||
| 92, | 42 | ||
| 250,908.00 | |||
| 204, | 54 | ||
| 77,897.00 | |||
| 43 | 197,012.00 | ||
| 51 | 195,126.00 | ||
| 177,100.00 | |||
| 83,2 | 30 | ||
| 58 | 140,012.00 | ||
| 48 | 265,296.00 | ||
| 189,420.00 | |||
| 235,872.00 | |||
| 230,724.00 | |||
| 59 | 238,655.00 | ||
| 138,560.00 | |||
| 259,680.00 | |||
| 93,208.00 | |||
| 33 | 91,212.00 | ||
| 36 | 153,216.00 | ||
| 77,308.00 | |||
| 56,496.00 | |||
| 106,6 | 52 | ||
| 44 | 242,748.00 | ||
| 195,858.00 | |||
| 178,560.00 | |||
| 190,876.00 | |||
| 98,528.00 | |||
| 169,572.00 | |||
| 79,420.00 | |||
| 167,928.00 | |||
| 215,705.00 | |||
| 146,350.00 | |||
| 10) | Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox. | ||
| 11) | Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error. | ||
| The strength of the correlation motivates further examination. | |||
| 12) | a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis. | ||
| b) Add to your chart: the chart name, vertical axis label, and horizontal axis label. | |||
| c) Complete the chart by adding Trendline and checking boxes | |||
| Read directly from the chart: | |||
| 13) | a) Intercept = | ||
| b) Slope = | |||
| c) R2 = | |||
| Perform Data > Data Analysis > Regression. | |||
| 14) | Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange | ||
| 15) | Use Excel to predict the number of minutes spent by a 22-year old shopper. Enter = followed by the regression formula. | ||
| Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results. | |||
| 16) | Is it appropriate to use this data to predict the amount of time that a 9-year-old will be on the Internet? | ||
| If yes, what is the amount of time, if no, why? |
Cleaning Data with Outlier
| 17) | On this worksheet, make an XY scatter plot linked to the following data: | ||||
| 1.01 | 2.8482 | ||||
| 1.48 | 4.2772 | ||||
| 1.8 | 4.788 | ||||
| 1.81 | 5.3757 | ||||
| 1.07 | 2.5252 | ||||
| 1.53 | 3.0906 | ||||
| 1.46 | 4.3362 | ||||
| 1.38 | 3.2016 | ||||
| 1.77 | 4.3542 | ||||
| 1.88 | 4.8692 | ||||
| 1.32 | 3.8676 | ||||
| 1.75 | 3.9375 | ||||
| 1.94 | 5.7424 | ||||
| 1.19 | 2.4752 | ||||
| 1.31 | 26.2 | ||||
| 1.56 | 4.5708 | ||||
| 1.16 | 2.842 | ||||
| 1.22 | 2.44 | ||||
| 1.72 | 5.1256 | ||||
| 1.45 | 4.3355 | ||||
| 1.43 | 4.2471 | ||||
| 3.5343 | |||||
| 5.46 | |||||
| 1.6 | 3.84 | ||||
| 1.58 | 3.8552 | ||||
| 18) | Add trendline, regression equation and r squared to the plot. | ||||
| Add this title. (“Scatterplot of X and Y Data”) | |||||
| 19) | The scatterplot reveals a point outside the point pattern. Copy the data to a new location in the worksheet. You now have 2 sets of data. | ||||
| Data that are more tha 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and must be investigated. | |||||
| It was determined that the outlying point resulted from data entry error. Remove the outlier in the copy of the data. | |||||
| Make a new scatterplot linked to the cleaned data without the outlier, and add title (“Scatterplot without Outlier,”) trendline, and regression equation label. | |||||
| Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R2? Explain why the slope and R Square change the way they did | |||||