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Course Project – B
Math-533 STATISTICS
EXAM
Speculation A: The average (mean) sales per week exceed 41.5 per salesperson : It has been speculated that an average sales per week exceeds 41. per salesperson. From our sample data the average (mean) sales per week for the given period was 42.34 sales. The analysis of the sample data showed that there is sufficient evidence to support the claim that the true average sale per week is greater than 41.5 per salesperson. This conclusion is further supported by the data which indicated (with 95% confidence), the actual average sales per week is somewhere between 41.6 and 43.2 per salesperson. The detail statistical analysis and methods used to support these conclusions are provided in the appendix. Key Statistics N Me a n
SE
Mea n Medi a n Mo d e St. De v Varianc e Ran g e Mi n Ma x 10 0
Step 1: Hypotheses Ho: μ ≤ 41.5 Ha: μ
Step 2: Level of Significance
Course Project – B α = 0. Z Value Z0.05 = 1. Step 3& 4: Calculation Z score Test – Single Tail (Result According to Minitab) One-Sample Z Snap Shoot of Minitab is attached in Appendix I
Course Project – B true proportion of salesperson who received online training will fall between 40% and 58 %. The detail is enclosed in appendix Step 1: Hypotheses
Course Project – B Ho: μ ≥ 0.55 Ha: μ <0. Step 2: Level of Significance α = 0. Z Value Z0.05 = 1. Step 3 and 4: Calculations Z score Test – Single Tail (Result According to Minitab) One-Sample Z Snap Shot of Minitab is enclosed in Appendix II Online trained Sales Employess = 50 Total Sample = Proportion of online trained Sales person from total sample is = 50/100 = 0. Test and CI for One Proportion Test of p = 0.55 vs p < 0. Sampl e X N Sample P 95% upper Bound
Z P
1 50 100 0.5 0.58^ -1.01^ 0.
Step 5: Decision Making Decision making rule according to p value is mentioned below as:
Course Project – B can be said that the proportion of sales persons who received online training is less than 55% is false. Speculation C: To check the average (mean) number of calls made per week by salespeople that had no training is less than 145. It has been speculated that the average mean number of calls made by untrained salesperson is less than 145. As per the sample data the average number of calls made by the untrained sales person is 141.35. The analysis of the data showed insufficient evidence to support the claim that the call made by untrained salesperson is less than 145. This conclusion is further supported by the data indicated (with 95% confidence) that the calls made by the untrained salesperson will fall between 137.02 and 145.14. The detail is enclosed in appendix. N Mean
SE
Mea n Medi a n Mod e St. De v Varianc e Ran g e
M
i n
M
a x 20
Step 1: Hypotheses Ho: μ ≥ 145 Ha: μ < 145 Step 2: Level of Significance α = 0.
Course Project – B Z Value Z0.05 = 1. Step 3 & 4: Calculations T test – Single Tail (Result According to Minitab)
Course Project – B analysis of the data showed that there is insufficient evidence to support the claim that an average call made is more than 15 minutes. This conclusion is further supported by the data indicated (with 95% confidence) that the average call time fall between 14.94 and 16.94. The detail analysis is enclosed in appendix.
Course Project – B Step 1: Hypotheses Ho: μ ≤ 145 Ha: μ
145 Step 2: Level of Significance α = 0. Z Value Z0.05 = 1.645 (taken from table) Step 3 & 4: Calculations Z score Test – Single Tail (Result According to Minitab) One-Sample Z Snap Shoot of Minitab is enclosed in Appendix IV One-Sample Z Test of μ = 15 vs > 15 The assumed standard deviation = 2. N Mean SE Mean 95% Lower Bound
Z P
Step 5: Decision Making The p value of this problem is 0.08 and it is more than 0.05 (α), therefore we are failed to reject the null hypothesis. The value of Z-score is
Course Project – B Appendix I Calculation for Speculation: A
