(THIS IS THE SECOND PART OF A PROJECT YOU COMPLETED FOR ME BEFORE, PLEASE SEE ATTACHED)
Complete the following four hypotheses, using a = 0.05 for each. The week 5 spreadsheet can be used in these analyses.
1. Mean sales per week exceed 42.5 per salesperson
2. Proportion receiving online training is less than 55%
3 Mean calls made among those with no training is at least 145
4. Mean time per call is 14.7 minutes
Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager’s belief. Use the Eight Steps of a Test of Hypothesis from Section 9.1 of your text book as a guide. You can use either the p-value or the critical values to draw conclusions. Be sure to explain your conclusion and interpret that to the claim in simple terms
Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals.
Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.
All DeVry University policies are in effect, including the plagiarism policy.
Project Part B report is due by the end of Week 6.
Project Part B is worth 100 total points. See grading rubric below.
Format for report:
Summary Report (about one paragraph on each of the four speculations)
Appendix with the calculations of the Eight Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas or spreadsheet screen shots used in the calculations.
Part B: Grading Rubric
Category
Points
Project Part A Report
Name
Institution
Introduction
The number of sales for any company in the sales and marketing industry is determined by several factors such as location and availability of customers. The project aims to analyze individual independent quantitative variables, Calls, Time, and Years and establish their relationship with Sales, the dependent variable. Additionally, the sales are divided into three types: Group, None, and Online, a qualitative variable. The analysis, comparison, and interpretation are done using graphs, numerical summaries, and descriptive statistics calculated using an Excel program.
1st Individual Variable (Sales(Y))
Sales is a quantitative variable since the values it takes can be counted or measured. The best form of a graph representing this variable is a boxplot, as shown below.
Figure 1: Boxplot of Sales
The boxplot above shows that the data for sales is approximately normally distributed since the mean, median, and mode are close or nearly equal. Additionally, the five-number summary used to construct the boxplot is given in the table below.
Table 1
Five Number Summary
Min 21
Q1 39
Q2 43
Q3 47
Max 67
The measure of central tendency that can best describe this type of distribution is the mean (M = 41.89) since the data does not contain outliers. The standard deviation of the distribution was 8.39, which is relatively small, indicating that most of the data points are concentrated around the mean.
2nd Individual Variable (Calls ())
The call is a quantitative variable that can be measured on an interval or ratio scale. The best form of a graph that can be used to represent a variable dataset is a histogram, as shown in the figure below.
Figure 2: Histogram for Calls
The histogram seems to be approximately normally distributed since the data’s mean, median, and mode are nearly the same. The mean (M = 162.1) is the appropriate measure of central tendency that can be used to describe the variable since the data does not contain outliers. Consequently, the standard deviation (SD = 17.99) is the appropriate measure of dispersion to describe the data since it shows how far the data values are from the mean.
3rd Individual variable (Time ())
Finally, Time is also a quantitative variable since it can be measured on an interval or ratio scale. The best graph that can represent the data associated with the variable is a boxplot, as shown in the figure below.
Figure 3: Boxplot of Time
The boxplot above can conclude that the data is approximately normally distributed since the mean, median, and mode are nearly identical. The five-number summary used to construct the boxplot is given in the table below.
Table 2
Five Number Summary
Min 10.0
Q1 13.6
Q2 14.95
Q3 16.9
Max 21.6
Further, the measure of central tendency appropriate for this distribution is the mean (M = 15.2) since the data does not contain outliers. The standard deviation (SD = 2.33) is the best measure of dispersion that describes how far or close the data points are from the mean. The standard deviation for this variable is relatively small, indicating that the data points are close to the mean.
1st Pairing of Variables
The first pairing of variables consists of quantitative variables: Calls () and Time (). A scatterplot can be used to show the relationship between the two variables, as shown in the figure below.
Figure 4: Scatterplot for Calls and Time
The scatter plot above shows no clear relationship between the two variables as the data points are close together without a clear pattern. The correlation coefficient, r = -0.281, suggests a weak negative linear association between calls and Time. In other words, as one decreases, the other one also decreases and vice versa.
2nd Pairing of Variables
The second pairing of variables consists of sales (Y) and Calls () quantitative variables. The appropriate graph that can be used to describe the relationship between the two variables is a scatterplot, as shown in the figure below.
Figure 5: Scatterplot for Sales and Calls
The scatterplot above indicates that there is approximately an upward relationship between the two variables. The correlation coefficient r = 0.3225 shows a weak, positive linear relationship between sales and calls. The regression line is given as Y = 17.5267 + 0.1503X. As the number of calls increases by one unit, the number of sales increases by 0.1503 units.
3rd Pairing of Variables
The third pairing of variables consists of Sales (Y), a quantitative variable, and type, a qualitative variable. The appropriate graphs that can be used to visualize the relationship between the two variables are boxplots, as shown below.
Figure 6: Boxplots for Sales and Type
The boxplots above show that Online Type of sales is the highest with a median sale of approximately 55, followed by Group with median sales of approximately 54, and None is the lowest with a median approximate sale of 36. Additionally, to compare whether or not there?s a significant difference in means between the type of sales, a one-way analysis of variance (ANOVA) was conducted, with the results given as = 2.9099, p = 0.0592 designating that there is no significant difference in means between the three types of sales.
Conclusion
In brief, using the graphical representations, numerical summaries, and statistical tests conducted on the individual variables and pairs of variables, there seems to be some association between sales and the other variables. Therefore, for any company to record a high number of sales, all the variables listed in the analysis must be considered.
%
Description
Addressing each speculation?20 points each
80 points
80%
Hypothesis test, interpretation, confidence interval, and interpretation
Summary report clarity
20 points
20%
One paragraph on each of the speculations
Total
100 points
100%
A quality paper will meet or exceed all of the above requirements.
