# 5 conclusion since we did not reject the null

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5. Conclusion: Since we did not reject the null hypothesis this indicates that there is not a statistically significant difference in the population means for Tim Tams sold in weeks with promotions and weeks with no promotions. There is insufficient evidence to identify a difference. *Since we rejected the null hypothesis this indicates that there is a statistically significant difference in the population mean weights for earrings produced by AJC and their competitor. Further , it appears that on average , AJC produce earrings that are lighter than their competitor’s. (This final sentence is determined by looking at the sample means shown in the first row of the table) Chi-squared test – Steps (Chi-squared test): Relationship between CATEGORICAL variables 1.Define the parameter: Not required 2. State the null and alternative hypothesis: H 0 : There is no relationship between industry and whether a profit was made. H A : There is a relationship between industry and whether a profit was made. 3. Determine and state the p-value, test the assumptions: p-value = 0.00798 *All of the expected cell counts are greater than one. Minimum is 5.42 * There are no expected cell counts less than five. Minimum is 5.42. * It was noted in the background that the data was randomly selected. 4.Decision: Since the p-value (0.00798) is less than 0.05, we reject the null hypothesis at the 5% significance level. 5.Conclusion: Since we rejected the null hypothesis this indicates that there is a statistically significant relationship between industry and whether a profit is made. Further, it appears as though a greater proportion of banking companies make profits compared to retail companies. ( The final sentence is determined by looking at the row or column proportions. Which is the actual and expected table to see what is the result) (In bar chart) If the shapes are different, then this is an indicator that there is a relationship. Practical vs Statistical Significance: Once a difference is determined, it is up to the practitioner do determine if the difference is of practical importance. This is done by weighing up the costs and benefits of acting on the knowledge of the difference. WEEK-11 CONFIDENCE INTERVALS Estimating a single value of a population parameter is to provide a point estimate/ For the population mean , it makes sense that our sample mean should be a good point estimate of the population mean/ Similarly our sample standard deviation should be a good point estimate of the population standard deviation . Focusing on the population mean , we have a Point Estimate of 297.04g. Our best estimate for the population mean is our point estimate, the sample mean. Lower Limit : (Point estimate – Margin) point estimate = mean Upper Limit : ((Point estimate + Margin) margin = confidence level Margin = t s n confidence Interval = lower & upper * The margin is a determined by the data’s standard deviation , sample size and how confident we want to be that the interval includes the (unknown) population mean. As we want to be 99% confident, we need to include a greater range of values that the population mean could
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