STATISTICS PROBLEMS

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Oreel55

Mathematics

BUS 308

ashford university

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Please provide assistance for week 2 problems 1-4. Also show work in cells where indicated . Additional dat information is listed in cell Q-V .

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ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Salary Compa- Midpoint ratio 59,9 27,8 34,8 58,9 47,9 76,4 41,4 22,5 73,7 21,8 23,9 64 41,6 24,1 24,2 45,5 69,8 36 24 33,5 76,4 59,4 22,9 60,3 23,7 22,7 43,6 74 73,9 48 23 27,7 61,2 26,8 22,7 23,1 23,6 57,3 35 24,2 1,050 0,897 1,122 1,033 0,997 1,141 1,036 0,979 1,100 0,948 1,037 1,123 1,041 1,046 1,053 1,138 1,224 1,162 1,042 1,080 1,140 1,238 0,994 1,256 1,031 0,989 1,089 1,104 1,103 1,001 1,001 0,893 1,074 0,863 0,989 1,004 1,025 1,006 1,130 1,052 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 Age 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 Performance Service Gender Rating 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 Raise Degree Gender1 5,7 3,9 3,6 5,5 5,7 4,5 5,7 5,8 4 4,7 4,8 4,5 4,7 6 4,9 5,7 3 5,6 4,6 4,8 6,3 3,8 3,3 3,8 4 6,2 3,9 4,4 5,4 4,3 3,9 5,6 5,5 4,9 5,3 4,3 6,2 4,5 5,5 6,3 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M 41 42 43 44 45 46 47 48 49 50 43,2 23,9 76,6 60,8 56,6 59,2 59 66,9 64,9 62,6 1,081 1,037 1,143 1,067 1,179 1,038 1,035 1,173 1,138 1,098 40 23 67 57 48 57 57 57 57 57 25 32 42 45 36 39 37 34 41 38 80 100 95 90 95 75 95 90 95 80 5 8 20 16 8 20 5 11 21 12 0 1 1 0 1 0 0 1 0 0 4,3 5,7 5,5 5,2 5,2 3,9 5,5 5,3 6,6 4,6 0 1 0 1 1 1 1 1 0 0 M F F M F M M F M M Grade E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A Do not manipuilate Data set on this page, copy to another page to make changes The ongoing question that the weekly assignments will focus on is: Are males and females paid the same Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work. The column labels in the table mean: ID – Employee sample number Salary – Salary in thousands Age – Age in years Performance Rating - Appraisal rating (employee evaluation scor Service – Years of service (rounded) Gender – 0 = male, 1 = female Midpoint – salary grade midpointRaise – percent of last raise Grade – job/pay grade Degree (0= BS\BA 1 = MS) Gender1 (Male or Female) Compa-ratio - salary divided by midpoint C A F E D E E E E E Week 1: Descriptive Statistics, including Probability While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will examining the issue using the salary measure. The purpose of this assignmnent is two fold: 1. Demonstrate mastery with Excel tools. 2. Develop descriptive statistics to help examine the question. 3. Interpret descriptive outcomes The first issue in examining salary data to determine if we - as a company - are paying males and females equally for descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not. 1 Descriptive Statistics: Develop basic descriptive statistics for Salary The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right. Then use Data Sort (by gender1) to get all the male and female salary values grouped together. a. Use the Descriptive Statistics function in the Data Analysis tab to develop the descriptive statistics summary for the overall group's overall salary. (Place K19 in output range.) Highlight the mean, sample standard deviation, and range. Using Fx (or formula) functions find the following (be sure to show the formula and not just the value in each cell) asked for salary statistics for each gender: Male Female Mean: 51,624 38,572 45,098 Sample Standard Deviation: 17,5041 18,9605 Range: 52,7 54,8 b. 2 Develop a 5-number summary for the overall, male, and female SALARY variable. For full credit, show the excel formulas in each cell rather than simply the numerical answer. Overall Males Females Max 36 76,4 76,6 3rd Q 60,9 63,3 76,6 Midpoint 43,4 58,9 33,5 1st Q 24,075 35,5 23,05 Min 21,8 23,7 76,6 3 Location Measures: comparing Male and Female midpoints to the overall Salary data range. For full credit, show the excel formulas in each cell rather than simply the numerical answer. Using the entire Salary range and the M and F midpoints found in Q2 a. What would each midpoint's percentile rank be in the overall range? b. What is the normal curve z value for each midpoint within overall range? * Professor I manually worked problem 3 to arrive at answers. I subtract the midpoint from the mean then divide by 4 Probability Measures: comparing Male and Female midpoints to the overall Salary data range For full credit, show the excel formulas in each cell rather than simply the numerical answer. Using the entire Salary range and the M and F midpoints found in Q2, find a. The Empirical Probability of equaling or exceeding (=>) that value for b. The Normal curve Prob of => that value for each group * Professor On the females I counted 5 Conclusions: What do you make of these results? Be sure to include findings from this week's lectu In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data se The relationship I see in the data in the 5-number summary is that both genders were closed when it came What does this suggest about our equal pay for equal work question? From looking at the results when it comes to salary females are exceeding at earning more than males. oint, our weekly assignments will focus on ng males and females equally for doing equal work is to develop some Place Excel outcome in Cell K19 Column1 Mean Standard Error 45,098 2,718857038 Median 43,4 Mode 76,4 Standard Deviation 19,22522248 Sample Variance 369,6091796 Kurtosis Skewness -1,491869384 0,187751611 Range 54,8 Minimum 21,8 Maximum Sum Count 76,6 2254,9 50 ll Salary data range. e numerical answer. Male 0,627 0,7179 Female 0,372 Use Excel's =PERCENTRANK.EXC function -0,6033 Use Excel's =STANDARDIZE function e midpoint from the mean then divide by the standard deviation. erall Salary data range e numerical answer. Male Female 18 32 Show the calculation formula = value/50 or =countif(range,">="&cell)/50 0,2356024 0,72684 Use "=1-NORM.S.DIST" function rofessor On the females I counted all numbers less than the midpoint 33.5 out of 50 numbers, For males I did the same action wi de findings from this week's lectures as well. ) see, to exist between the data sets? enders were closed when it came to the MAX results in the 5- number summary. The range for both genders salary data were slig g at earning more than males. Gender1 Salary M 76,4 M 76,4 M 73,9 M 73,7 M 64,9 M 64 M 62,6 M 61,2 M 60,8 M 59,9 M 59,2 M 59 M 58,9 M 57,3 M 48 M 47,9 M 45,5 M 43,6 M 43,2 M 27,8 M 27,7 M 26,8 M 24,2 M 24 M 23,7 F 76,6 F 74 F 69,8 F 66,9 F 60,3 F 59,4 F 56,6 F 41,6 F 41,4 F 36 F 35 F 34,8 F 33,5 F 24,2 F 24,1 F 23,9 F 23,9 F 23,6 76,4 23,7 52,7 76,6 21,8 54,8 F F F F F F F 23,1 23 22,9 22,7 22,7 22,5 21,8 r males I did the same action with the male midpoint of oth genders salary data were slightly close as well. I found that all the statistical data listed diferred amongst each other. d amongst each other. Week 2: Identifying Significant Differences - part 1 To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders in What we do, depends upon our findings. 1 As with the compa-ratio lecture example, we want to examine salary variation within the groups - are they a What is the data input ranged used for this question: b c. Which is needed for this question: a one- or two-tail hypothesis statement and test ? Answer: Why: Step 1: Step 2: Step 3: Step 4: Step 5: Ho: Ha: Significance (Alpha): Test Statistic and test: Why this test? Decision rule: Conduct the test - place test function in cell k10 Step 6: Conclusion and Interpretation What is the p-value: What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the variance in the population for male and female salaries? 2 Once we know about variance quality, we can move on to means: Are male and female average salaries eq (Regardless of the outcome of the above F-test, assume equal variances for this test.) a b c. What is the data input ranged used for this question: Does this question need a one or two-tail hypothesis statement and test? Why: Step 1: Ho: Ha: Step 2: Significance (Alpha): Step 3: Test Statistic and test: Why this test? Step 4: Decision rule: Step 5: Conduct the test - place test function in cell K35 Step 6: Conclusion and Interpretation What is the p-value: What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the means in the population for male and female salaries? 3 Education is often a factor in pay differences. Do employees with an advanced degree (degree = 1) have higher average salaries? Note: assume equal variance for the salaries in each degree for this question. a What is the data input ranged used for this question: b c. Step 1: Step 2: Step 3: Step 4: Step 5: Does this question need a one or two-tail hypothesis statement and test? Why: Ho: Ha: Significance (Alpha): Test Statistic and test: Why this test? Decision rule: Conduct the test - place test function in cell K60 Step 6: Conclusion and Interpretation What is the p-value: Is the t value in the t-distribution tail indicated by the arrow in the Ha claim? What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the impact of education on average salaries? 4 Considering both the compa-ratio information from the lectures and your salary information, what conclus Why - what statistical results support this conclusion? olves either showing where the data you used is located mns from the data tab to the right for your use this week. between the genders involves equality - are they the same or different? Use Cell K10 for the Excel test outcome location. Use Cell K35 for the Excel test outcome location. Use Cell K60 for the Excel test outcome location. ormation, what conclusions can you reach about equal pay for equal work? Male 0,897 Female 1,122 1,033 1,036 0,997 0,979 1,141 0,948 1,100 1,037 1,123 1,041 1,138 1,046 1,042 1,053 1,140 1,224 1,031 1,162 1,089 1,080 1,103 1,238 1,001 0,994 0,893 1,256 1,074 0,989 0,863 1,104 1,006 1,001 1,052 0,989 1,081 1,004 1,067 1,025 1,038 1,130 1,035 1,037 1,138 1,143 1,098 1,179 1,173 Compa- Gender1 Salary Degree ratio 1,122 F 34,8 1 1,036 F 41,4 1 0,979 F 22,5 1 0,948 F 21,8 1 1,037 F 23,9 1 1,041 F 41,6 0 1,046 F 24,1 1 1,053 F 24,2 1 1,224 F 69,8 1 1,162 F 36 0 1,080 F 33,5 0 1,238 F 59,4 1 0,994 F 22,9 0 1,256 F 60,3 0 0,989 F 22,7 0 1,104 F 74 0 1,001 F 23 1 0,989 F 22,7 0 1,004 F 23,1 0 1,025 F 23,6 0 1,130 F 35 0 1,037 F 23,9 1 1,143 F 76,6 0 1,179 F 56,6 1 1,173 F 66,9 1 1,050 M 59,9 0 0,897 M 27,8 0 1,033 M 58,9 1 0,997 M 47,9 1 1,141 M 76,4 1 1,100 M 73,7 1 1,123 M 64 0 1,138 M 45,5 0 1,042 M 24 1 1,140 M 76,4 1 1,031 M 23,7 0 1,089 M 43,6 1 1,103 M 73,9 0 1,001 M 48 0 0,893 M 27,7 0 1,074 M 61,2 1 0,863 M 26,8 1 1,006 1,052 1,081 1,067 1,038 1,035 1,138 1,098 M M M M M M M M 57,3 24,2 43,2 60,8 59,2 59 64,9 62,6 0 0 0 1 1 1 0 0 Week 3: Identifying Significant Differences - part 2 To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh or showing the excel formula in each cell. Be sure to copy the appropriate data columns from 1 A good pay program will have different average salaries by grade. Is this the case for our company? a What is the data input ranged used for this question: Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question. b. Step 1: Step 2: Step 3: Step 4: Step 5: Ho: Ha: Significance (Alpha): Test Statistic and test: Why this test? Decision rule: Conduct the test - place test function in cell K08 Step 6: Conclusion and Interpretation What is the p-value: What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the means in the population for grade salaries? 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? (Use the values from the ANOVA table to complete the follow table.) Groups Compared Mean Diff. T value used +/- Term Low A-B A-C A-D A-E A-F B-C B-D B-E B-E C-D C-E C-F D-E D-F E-F 3 One issue in salary is the grade an employee is in - higher grades have higher salaries. This suggests that one question to ask is if males and females are distributed in a similar pattern across the a What is the data input ranged used for this question: b. Step 1: Step 2: Step 3: Step 4: Step 5: Ho: Ha: Significance (Alpha): Test Statistic and test: Why this test? Decision rule: Conduct the test - place test function in cell K54 Step 6: Conclusion and Interpretation What is the p-value: What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the means in the population for male and female salaries? 4 What implications do this week's analysis have for our equal pay question? Why - what statistical results support this conclusion? This involves either showing where the data you used is located he appropriate data columns from the data tab to the right for your use this week. he case for our company? Use Cell K08 for the Excel test outcome location. ate, for purposes of this question. to High Difference Significant? Why? Use Cell K54 for the Excel test outcome location. Place the actual distribution in the table below. A B C D Male Female E Place the expected distribution in the table below. A B C D E Male Female Data Input Table: Group name: List salaries within each grade A B Salary Range Groups C D F F nge Groups E F Week 4: Identifying relationships - correlations and regression To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data t 1 What is the correlation between and among the interval/ratio level variables with salary? (Do not include c a. Create the correlation table. i. What is the data input ranged used for this question: ii. Create a correlation table in cell K08. b. Technically, we should perform a hypothesis testing on each correlation to determine if it is significant or not. However, we can be faithful to the process and save some time by finding the minimum correlation that would result in a two tail rejection of the null. We can then compare each correlation to this value, and those exceeding it (in either a positive or negative direction) can be considered statistically significant. i. What is the t-value we would use to cut off the two tails? T= ii. What is the associated correlation value related to this t-value? r = c. What variable(s) is(are) significantly correlated to salary? d. Are there any surprises - correlations you though would be significant and are not, or non significant cor e. Why does or does not this information help answer our equal pay question? 2 Perform a regression analysis using salary as the dependent variable and the variables used in Q1 along wi our two dummy variables - gender and education. Show the result, and interpret your findings by answerin Suggestion: Add the dummy variables values to the right of the last data columns used for Q1. What is the multiple regression equation predicting/explaining salary using all of our possible variables ex a. What is the data input ranged used for this question: b. Step 1: State the appropriate hypothesis statements: Ho: Ha: Step 2: Significance (Alpha): Step 3: Test Statistic and test: Why this test? Step 4: Decision rule: Step 5: Conduct the test - place test function in cell M34 Step 6: Conclusion and Interpretation What is the p-value: What is your decision: REJ or NOT reject the null? Why? What is your conclusion about the factors influencing the population compa-ratio values? c. If we rejected the null hypothesis, we need to test the significance of each of the variable coeff Step 1: State the appropriate coefficient hypothesis statements: (Write a single pair, we Ho: Ha: Step 2: Significance (Alpha): Step 3: Test Statistic and test: Why this test? Step 4: Decision rule: Step 5: Conduct the test Note, in this case the test has been performed and is part of the Regression output a Step 6: Conclusion and Interpretation Place the t and p-values in the following table Identify your decision on rejecting the null for each variable. If you reject the null, Midpoint Age Perf. Rat. Seniority Raise Gender t-value: P-value: Rejection Decision: If Null is rejected, what is the variable's coefficient value? Using the intercept coefficient and only the significant variables, what is the equation? Salary = d. Is gender a significant factor in compa-ratio? e. Regardless of statistical significance, who gets paid more with all other things being equal? f. How do we know? 3 After considering the compa-ratio based results in the lectures and your saalary based results, what else wo before answering our question on equal pay? Why? 4 Between the lecture results and your results, what is your answer to the question of equal pay for equal work for males and females? Why? 5 What does regression analysis show us about analyzing complex measures? lves either showing where the data you used is located olumns from the data tab to the right for your use this week. lary? (Do not include compa-ratio in this question.) Use Cell K08 for the Excel test outcome location. , or non significant correlations you thought would be? es used in Q1 along with ur findings by answering the following questions. r possible variables except compa-ratio? Use Cell M34 for the Excel test outcome location. ch of the variable coefficients. Write a single pair, we will use it for each variable separately.) he Regression output above. If you reject the null, place the coefficient in the table. Degree s the equation? things being equal? d results, what else would you like to know
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