In the following video, Prof. Tricha will walk you through a real-life example of how confidence intervals can be used to make decisions.

Let’s consider another example of how you can use confidence intervals to make a decision. Recall the Facebook example discussed in the last session. Let’s find the 90% confidence interval (confidence interval for a 90% confidence level) for that case.

Recall that 50.5% of the 10,000 people surveyed preferred feature B to feature A. So, if X = the proportion of people that prefer feature B to feature A, then, for this sample, = 0.505 (50.5%) and n = 10,000. In addition to this, you’ve been told that the sample’s standard deviation S = 0.2(20%).

Also, you know that the actual population mean

lies between

+ margin of error. However, now it is vital for us to find this margin of error.

If this margin of error is, say, 1%, then that means that the population mean

, which is the proportion of people that prefer feature B to feature A, lies between the range (50.5 – 1)% to (50.5 + 1)%, i.e., 49.5 % to 51.5%. This means that you cannot say with certainty that would be more than 50%. So, even though the proportion of people that prefer feature B to feature A is more than 50% in our sample, you would not be able to say with certainty that this proportion would be more than 50% for the entire population.

On the other hand, if the margin of error is, say, 0.3%, then you will be able to say that the population mean lies within (50.5 – 0.3)% and (50.5 + 0.3)%, i.e., 50.2% to 50.8%. So, you will be able to say with certainty that the proportion of people that prefer feature B to feature A is more than 50% in our sample and for the entire population too.

- Now, the margin of error corresponding to a 90% confidence level would be given by = 0.0033 (0.33%), and the population mean lies between 50.17% and 50.83%.

- Hence, you can say that feature B should replace feature A with 90% confidence.