Keller MATH 533 Course Project Part B, Exams of Nursing

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Hypothesis Testing MATH – 533

Hypotheses testing involves the testing of the null hypothesis and the alternative hypothesis. When testing the hypothesis either the null hypothesis or the alternative hypotheses is rejected. The value to a company knowing to accept or reject a hypothesis will aid in the decision making process. Information derived from hypothesis testing can aid in more timely decision. Requirement A: The average (mean) sales per week exceeds 41.5 per salesperson. Key Statistics as computed by Minitab Variable N N* Mean SE Mean StDev Minimum Q1 Median Q SALES 100 0 42.340 0.417 4.171 32.000 39.250 42.000 45. Variable Maximum Range IQR N for Mode Mode SALES 52.000 20.000 5.750 44 12 Step 1 Hypotheses Ho: μ = 41. Ha: μ > 41. Step 2 Level of Significance The a = 0.05 is given. Step 3 Identify the statistical test to use. Use z-test because StDev is known and the sample (n=100) is a large sample (n > 30). The test done if to accept or reject that sales will exceed 41.5 per salesperson per week. To test this, a single tail test will be performed. Z score Test – Single Tail (Result According to Minitab) One-Sample Z = 2.01 and P =. 022 One-Sample Z: SALES

Step 2 Level of Significance The a = 0.05 is given. Step 3 Identify the statistical test to use. Use 1 Proportion because StDev is known and the sample (n=50) is a large sample (n > 30). 1Proportion score Test – Single Tail One Proportion- Z = - 1.01 and a P-Value of 0.157. Step 4 Decision Rule The alternative hypothesis states that the true population proportion of salespeople that received online training is less than 55%. This will be a one tailed test to the left. The given a = .05 is to the right of Z = - 1.645. Thus we reject the null hypothesis if Z> - 1.645. Step 5 Decision Making The online trained salesperson mean is 45.340. The computed, using Minitab, Z score

• 1.01 and P value of 0.157. The computed Z score is greater than - 1.645, reject the null hypothesis. We can be 95% confident that the true population mean that received online training will fall within the Confidence Interval (CI) of 0.4020, 0.5980. As a manager you expect that 45.34% of salespersons will have received online training. Requirement C: The average (mean) number of calls made per week by salespeople that had no training is less than 145. Step 1 Hypotheses

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Ho: μ = 145 Ha: μ < 145 Step 2 Level of Significance The a = 0.05 is given. Step 3 Identify the statistical test to use. Use On-Sample T-test because StDev is known and the sample (n=20) is a small sample (n < 30). This will be a one tailed test to the left. T score Test – Single Tail test to the left (Result According to Minitab) One-Sample T = - 1.76 and P =. Step 4 Decision Rule The alternative hypothesis states Less than less than 145 calls, on average, are made by salespeople that have had no training. The given a = .05 is to the right of Z = - 1.645. Thus we reject the null hypothesis if Z > - 1.645. If the P value is more than the given a of .05 then rejecting the null hypothesis is supported by the evidence. Step 5 Decision Making The average number of calls made by salespeople that received no training is 141.35. The computed T score is - 1.76 and the P value is .047, which is less than the given a of.

1. The alternative hypothesis can be affirmed that mean number of calls made per week by salespeople that have not received training is less than 145.. The computed Minitab

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1.645. We accept the alternative hypothesis that the average call time is greater than 15 minutes. Step 5 Decision Making The sample of 100 calls yielded an average time of calls made of 15.341 minutes. The computed Z score is 1.41 and the P value is .079, which is greater than the given a of.

1. The null hypothesis is affirmed. The average time of calls is not greater than 15 minutes. The P value is greater than the a, which gives further evidence to reject the alternative hypothesis. Management can expect that the average time spent on a call in not greater than 15 minutes. The computed mean time is 15.34. This time falls within the 95 % confidence interval of 14.523, 16.159. We can be 95 % certain that the average time of a call will be between 14.523 and 16.159 minutes long. Appendix I Calculation for Ans. A Descriptive Statistics: SALES, CALLS, TIME, YEARS Variable N N* Mean SE Mean StDev Minimum Q1 Median Q SALES 100 0 42.340 0.417 4.171 32.000 39.250 42.000 45. CALLS 100 0 162.09 1.80 18.01 124.00 149.00 160.50 176. TIME 100 0 15.341 0.242 2.415 10.000 13.500 15.050 17. YEARS 100 0 2.080 0.124 1.236 0.000 1.000 2.000 3. Variable Maximum Range IQR Mode N for Mode SALES 52.000 20.000 5.750 44 12 CALLS 201.00 77.00 27.75 149 6 TIME 21.600 11.600 3.500 14.6, 14.8 4 YEARS 5.000 5.000 2.000 2 32 One-Sample Z: SALES Test of mu = 41.5 vs > 41. The assumed standard deviation = 4.

95% Lower Variable N Mean StDev SE Mean Bound Z P SALES 100 42.340 4.171 0.417 41.654 2.01 0. One-Sample Z The assumed standard deviation = 4. N Mean SE Mean 95% CI 100 42.340 0.417 (41.522, 43.158) Appendix II Descriptive Statistics: SALES, CALLS, TIME, YEARS Variable TYPE N N* Mean SE Mean StDev Minimum Q1 Median Distribution Plot Density SALES GROUP 30 0 40.833 0.381 2.086 37.000 39.000 41. NONE 20 0 37.100 0.502 2.245 32.000 36.250 37. ONLINE 50 0 45.340 0.421 2.973 41.000 43.000 45. CALLS GROUP 30 0 156.57 2.51 13.74 131.00 149.75 154. NONE 20 0 141.35 2.07 9.26 124.00 134.00 143.

Appendix III Descriptive Statistics: CALLS Variable TYPE N N* Mean SE Mean StDev Minimum Q1 Median CALLS GROUP 30 0 156.57 2.51 13.74 131.00 149.75 154. NONE 20 0 141.35 2.07 9.26 124.00 134.00 143. ONLINE 50 0 173.70 1.89 13.38 149.00 162.50 174. Variable TYPE Q3 Maximum Range IQR Mode N for Mode CALLS GROUP 166.50 192.00 61.00 16.75 149, 150, 152, 154 2 NONE 148.25 157.00 33.00 14.25 134, 143, 146, 149 2 ONLINE 184.25 201.00 52.00 21.75 178 4 One-Sample T Test of mu = 145 vs < 145 95% Upper N Mean StDev SE Mean Bound T P Distribution Plot

Density 20 141.35 9.26 2.07 144.93 - 1.76 0. One-Sample T N Mean StDev SE Mean 95% CI 20 141.35 9.26 2.07 (137.02, 145.

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Appendix IV Descriptive Statistics: TIME Variable N N* Mean SE Mean StDev Minimum Q1 Median Q TIME 100 0 15.341 0.242 2.415 10.000 13.500 15.050 17. N for Variable Maximum Range IQR Mode Mode TIME 21.600 11.600 3.500 14.6, 14.8 4 One-Sample Z: TIME Test of mu = 15 vs > 15 The assumed standard deviation = 2. Variable N Mean StDev SE Mean 95% Lower Bound Z P TIME 100 15.341 2.415 0.241 14.944 1.41 0. One-Sample Z: TIME The assumed standard deviation = 4. Variable N Mean StDev SE Mean 95% CI Distribution Plot

Density