Lower bound and upper bound



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Hi All, I am not able to understand how to calculate upper and lower bound in above question. Thanks in advance.

Thanks & Regards, Anshul Singhal





Kushoni and Andrey,

With the details of the question provided above, you don't have enough information to calculate the standard deviation and therefore, cannot get an exact margin of error and the confidence interval. But you can eliminate some of the answers with a solid understanding of the pieces at play here.

For Experience B, there are two options for the Lower Bound of the Confidence Interval. Both cannot be correct, so we will decide which answer is correct between these two. With RPV as the KPI, we're looking at the +1.2% RPV LIFT with only 61% confidence (1 minus the p-value of 0.39). That 1.2% is the calculated mean, such that the Lower Bound must fall below the mean by definition. Therefore we can rule out answer A with +2%.

Similarly, for Experience C, there are two options for the Upper Bound. The higher confidence interval will be wider, as it means the interval needs to capture a larger portion of the population. We also know that Experience C is currently sitting at a strong 94% confidence level, so the -4.3% RPV LIFT is relatively trustworthy. With both of those considerations, Answer D with upper bound of the 90% confidence interval at +3% is beyond the more reasonable -1% for the 95% confidence Interval. So we eliminate Answer D.

And so, to answer the question around the calculating the lower and upper bound for the confidence interval, you'll need the mean of the data (RPV in this case) and the standard deviation of the data (average of the squared differences from the mean, for each order). From there, using the desired confidence level and sample size, you can calculate the margin of error, which give you the mean +/- values for the upper and lower bound.

I hope that helps.