Part B Hypothesis Testing & Confidence Intervals

Introduction

This is an amateur attempt to view, analyze, interpret, and present a numerical summary of a data file that includes five variables found in a call center. The five variables are as follows:

· SALES(Y) represents the number sales made this week.

· CALLS(X1) represents the number of sales calls made this week.

· TIME(X2) represents the average time per call this week.

· YEARS(X3) represents years of experience in the call center.

· TYPE represents the type of training the employee received.

Initially we were presented with 100 lines of data that displayed the following 5 variables. Here is a sample of the data below. I have attached all of my excel spreadsheet analysis as well for further review in the .

The first 4 variables are quantitative variables in that they occur naturally as numbers. Whereas the last item, Type is considered a qualitative variable. It is categorical in nature. In an effort to compare the qualitative to the quantitative, numbers have been assigned to the qualitative data, which we will discuss in the body of the paper.

Today, we will present the data, analyzed each variable by itself using graphical and numerical techniques. In addition, we will present in Excel images the results and graphs. In addition, we will discuss the appropriate measures of central tendencies, measures of dispersion and shapes of the distributions as well.

We will include also key data which will include the Min, Q1, Median, Q3, and the Max, in as well as some other data as well.

Finally, out of the 5 variables above 3 pairings of the data has been done and the correlation will be calculated, interpreted, and discussed in terms of the past present and future. The pairing to be discussed will be as follows:

· Correlation Between Calls(x1) and Sales (Y)

· Correlation Between Calls (x1) and Years (X3)

· Correlation between Type of Training and Sales (Y)

The goal is to discuss the 3 possible correlations between 2 sets of variables and discuss how they appear and how they can be viewed in the future.

Analysis of Sales (Y)

Based on the 100 sampled sales in the call center, the sales had a range between 34 and 54, the calculated range and mean and std deviation are as follows in the chart below.

Once the data was plotted and placed on a histogram, you can see that the majority of the sales were in the range of 42 to 46 sales made per week. The sales actually had a 40% increase in this range and then it began to fall off. The Mean of 44.34 and the Median of 44 were in this Bin as well, which means that the sales exhibited a right tail and this is a rightward skewed data set. The Median is also slightly less than the mean as well.

Analysis of Calls (X1)

Based on the 100 samples of calls that were analyzed and received weekly, we discovered that on average the weekly calls were approximately 157 calls. The Mean was 159 as well. The MIN calls was 121 and the Max was 198. Here the data of the median and the mean fell close together as well, however the histogram is rightward skewed as well and the tail is to the right.

Analysis of Time (X2)

Here after looking at 100 sample items I discovered something different with Time. I noticed that time spent on the phone was about 17% of the time between 15 to 16 minutes. The other bins were substantially lower. In addition, the average time spent on the phone was 15.54. The median was 15.3. The most time spent on the phone was 22 minutes. The tail here is slightly skewed to the right, and in the last bin only 3% of the employees spend more than 20 minutes on the phone. The skewness of 0.12 confirms the tail being to the right and this confirms the median is less than the mean. In addition, the sd is 2.64, so typically an average call will only deviate about 2.64 + or -.

Analysis of Pairing Sales and Calls

Here it was discovered that the correlation between Sales made weekly and the number of calls made weekly were directly correlated. The correlation was measured at 0.871344.

In addition, the trend is close to 100% and therefore the correlation is direct. We also estimated that this will be the same in the future as well. However, given more time we may able to see the point where the is no correlation given other factors.

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Correlation Between Calls (x1) and Years (X3

The correlation between calls made and the number of years in call center almost had zero correlation. The data states that the correlation is -0.00745. There is almost no correlation.

Correlation between Type of Training and the Sales

As a result of paring the type of training with the sales. We made an interesting discovery. First of all, the Type of training was qualitative data and had to be changed to a numerical system. The following numbers were assigned to our data.

Please keep in mind that for Training this was the original spread of the data.

When the Type of training (ONLINE< GROUP or NONE) was compared to sales we discovered and indirect relationship. Meaning that the correlation was -0.60548

. In the Plot graph above please notice that the higher the sales then the lower the number of training. Meaning that those with a 1 or 2 for training actually have higher sales, when compared to those that had no training (3).

Recommendation

I recommend that we identify the employees that have had no training and consider investing in implementation of a training program. As a direct result the overall sales of the call center will increase.

Correlation Between Calls(x1) and Sales (Y)

Sales (Y)

168 131 162 183 177 181 123 169 158 146 178 142 137 195 146 165 121 146 132 182 151 146 190 150 149 167 189 162 147 171 165 175 161 188 136 135 168 167 150 151 141 131 174 154 131 128 126 180 166 152 179 140 154 164 139 165 172 147 152 160 159 186 150 155 157 170 175 186 181 171 185 146 156 157 163 175 175 173 140 156 146 148 183 191 149 143 185 136 198 153 129 158 149 175 154 151 153 167 167 143 48 36 46 47 44 49 35 46 44 39 48 42 45 54 43 44 34 44 40 51 41 45 52 39 41 45 46 47 42 45 44 50 46 53 39 39 48 46 43 44 42 39 49 41 42 39 37 46 45 44 50 39 43 45 42 44 45 41 43 48 42 46 46 43 45 48 45 49 51 47 50 39 42 46 43 54 51 50 41 43 40 42 50 49 40 40 47 41 51 43 38 44 43 47 40 43 46 46 46 39

Correlation Between Calls (x1) and Years (X3)

Years (X3)

168 131 162 183 177 181 123 169 158 146 178 142 137 195 146 165 121 146 132 182 151 146 190 150 149 167 189 162 147 171 165 175 161 188 136 135 168 167 150 151 141 131 174 154 131 128 126 180 166 152 179 140 154 164 139 165 172 147 152 160 159 186 150 155 157 170 175 186 181 171 185 146 156 157 163 175 175 173 140 156 146 148 183 191 149 143 185 136 198 153 129 158 149 175 154 151 153 167 167 143 5 4 3 3 3 2 3 3 1 3 4 0 2 2 0 3 2 1 1 2 1 3 3 0 3 4 1 3 3 2 0 3 3 2 0 1 5 0 3 2 3 2 0 4 3 1 4 4 5 2 3 1 1 3 2 2 3 3 1 2 4 3 2 3 4 1 2 1 4 2 0 1 2 2 1 1 2 1 3 2 2 2 1 2 4 2 2 3 1 3 3 3 1 2 3 1 0 1 0 3

Correlation betwee Type of Training and the Sales

Type

48 36 46 47 44 49 35 46 44 39 48 42 45 54 43 44 34 44 40 51 41 45 52 39 41 45 46 47 42 45 44 50 46 53 39 39 48 46 43 44 42 39 49 41 42 39 37 46 45 44 50 39 43 45 42 44 45 41 43 48 42 46 46 43 45 48 45 49 51 47 50 39 42 46 43 54 51 50 41 43 40 42 50 49 40 40 47 41 51 43 38 44 43 47 40 43 46 46 46 39 1 3 3 1 1 1 3 2 2 2 1 1 1 1 1 1 3 3 3 1 3 1 1 2 2 2 2 1 2 1 1 1 2 1 3 1 1 1 2 2 3 3 1 3 2 2 3 3 3 1 1 3 1 1 3 3 2 2 2 1 2 2 2 1 1 1 2 2 2 1 1 2 2 1 2 1 1 1 3 1 3 2 2 2 1 3 1 2 1 2 3 1 2 2 2 2 1 1 1 3

Type

COUNT

Online Group None 44 34 22

Calls (X1) 168 131 162 183 177 181 123 169 158 146 178 142 137 195 146 165 121 146 132 182 151 146 190 150 149 167 189 162 147 171 165 175 161 188 136 135 168 167 150 151 141 131 174 154 131 128 126 180 166 152 179 140 154 164 139 165 172 147 152 160 159 186 150 155 157 170 175 186 181 171 185 146 156 157 163 175 175 173 140 156 146 148 183 191 149 143 185 136 198 153 129 158 149 175 154 151 153 167 167 143