assignment 2

# assignment 2 - BUSINESS ANALYTICS BUS1BAN ASSIGNMENT 2...

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BUSINESS ANALYTICS BUS1BAN ASSIGNMENT 2: STATISTICAL INFERENCE AND REGRESSION ANALYSIS QUESTION 1: a/ The mean and standard deviation of Rejoice Sales: Rejoice Sales Mean 502.6534615 Standard Error 37.53110753 Median 378.95 Mode #N/A Standard Deviation 270.6406653 Sample Variance 73246.3697 Kurtosis -0.065859259 Skewness 1.187308771 Range 914.82 Minimum 219.4 Maximum 1134.22 Sum 26137.98 Count 52 Confidence Level (90.0%) 62.87529962 b/ The 90% interval estimate of the average weekly sales for Rejoice: µ = = 502.6535 × = 502.6535 1.6753 = 502.6535 62.8759 = [439.7776, 565.5294] c/ Using a level of significance of α = 0.05 test whether the average of the weekly sales for Rejoice are more than 450 kgs: Step 1: Hypothesis : µ = 450 : µ > 450 Step 2: Test Statistic t = Step 3: Level of Significance α = 0.05 1

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Step 4: Decision Rule (1) (2) Critical value = = = 1.6753 (3) Reject if t > 1.6753 Step 5: Value of Test Statistic t = = = = 1.40 Step 6: Conclusion Since the test statistic 1.4029 is not the rejection region, we cannot reject in favour of at the 5% significance level and conclude that there is insufficient evidence to infer that the average of the weekly sales for Rejoice is more than 450 kgs. d/ Briefly explain what a Type I error and what a Type II error are and their consequences in this problem: A Type I error occurs if we reject when in fact it is true and should not be rejected. A Type II error occurs if we do not reject when in fact it is false and should be rejected. Consequences of Type I error: we conclude that the average of weekly sales for Rejoice is not more than 450 kgs when in fact it is true. Consequence of Type II error: we conclude that the average of weekly sales for Rejoice is more than 450 kgs when in fact it is false. e/ Find the p-value The p-value = P (z > 1.40) = P (z < -1.40) = 0.0808 Explain what the p-value is and how we could use the p-value to test the hypotheses: The p-value provides information about the amount of statistical evidence that supports the alternative hypothesis.
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