Hypothesis Testing and Confidence Intervals in Applied Managerial Statistics, Assignments of Mathematics

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Course Project Part

B: Hypothesis

Testing and

Confidence Intervals

Course Name: MATH534 Applied Managerial Statistics

Student Name: XXX

Part B: Hypothesis Testing and Confidence Intervals Brief Introduction This is Project Part B: Hypothesis Testing and Confidence Intervals. In this part of project, we will conduct Hypothesis Testing for a few of variables and data set. Confidence Intervals will also be found for those variables.

1. Mean sales per week exceed 42.5 per salesperson

1. Hypothesis Testing ▪ H 0 : μ ≤42. ▪ Hα: μ >42.5 (claim) ▪ We will conduct right-tailed t-test since the population standard deviation sigma ( σ^ )is unknow. ▪ Identifying the Rejection Region ▪ Since α=0.05 and df=n-1=100-1=99 the t-critical value will be: 1. Sales (Y) Mean 43. Standard Error 0. Median 42. Mode 41. Standard Deviation 7. Sample Variance 55. Kurtosis 2. Skewness 1. Range 37. Minimum 30. Maximum 67.

Sum 0 Count 100. Finding the test statistic: t = x ´ − μ =1. S

√ n

, t=1.519<1.660.

Since the p-value, 0.0079, is greater than α, 0.05, we fail to reject H-null. We do have enough evidence to support the claim. Hence, the proportion of receiving online training is less than 55%

2. Compute 99% confidence intervals for Training Type used in hypothesis test and interpret these intervals. We are 99% confident that the actual population proportion of receiving online training will be between (0.302, 0.558). 3.Mean calls made among those with no training is at least 145
3. Hypothesis Testing ▪ H0: μ ≥145 (claim) ▪ Hα: μ < 145 ▪ Since n=20 < 30, and the population distribution is unknown. The z or t Hypothesis Testing cannot be conducted based on the Central Limit Theorem.
4. Compute 99% confidence intervals for with mean calls made among those with no training is at least 145 Calls for No Training Mean 144. 0 Standard Deviation 15. Training Type Count GROUP 37 NONE 20 ONLINE 43 Total 100

We are 99% confident that the actual population mean for calls time will be between (14.34, 15.56) minutes. Summary From the Hypothesis Testing conducted and Confidence Intervals found above, the summary of results is following:

1. Mean sales per week may not exceed 42.5 per salesperson. We are 99% confident that the actual population mean will be between (41.68, 45.58).
2. The proportion of receiving online training is less than 55%. We are 99% confident that the actual population proportion of receiving online training will be between (0.302, 0.558).
3. We are 99% confident that the actual population mean of calls for those with no training will be between (134, 154) calls.
4. The mean time per call is 14.7 minutes. We are 99% confident that the actual population mean for calls time will be between (14.34, 15.56) minutes.