Explanation: The conclusion that is accurate at a 95% confidence interval is that in general, users who visit the new website are more likely to make a purchase. A 95% confidence interval means that we are 95% confident that the true difference between the two groups lies within a certain range of values. To calculate the 95% confidence interval, we can use the following formula:
CI = (p1 - p2) ± 1.96 * sqrt(p * (1 - p) * (1/n1 + 1/n2))
where p1 and p2 are the conversion rates for the test and control groups, respectively, p is the pooled conversion rate, n1 and n2 are the sample sizes for the test and control groups, respectively, and 1.96 is the z-score for a 95% confidence level.
Using this formula, we can calculate the 95% confidence interval for each country as follows:
Country | p1 | p2 | n1 | n2 | p | CI United States | 0.12 | 0.11 | 2000 | 2000 | 0.115 | (-0.006, 0.026) Germany | 0.06 | 0.04 | 1000 | 1000 | 0.05 | (-0.002, 0.042) United Kingdom | 0.09 | 0.07 | 1500 | 1500 | 0.08 | (-0.003, 0.053) France | 0.08 | 0.08 | 1200 | 1200 | 0.08 | (-0.024, 0.024) Canada | 0.05 | 0.03 | 800 | 800 | 0.04 | (-0.005, 0.045)
We can see that for all countries except France, the confidence interval does not include zero, which means that the difference between the test and control groups is statistically significant at a 95% confidence level. However, this does not mean that the difference is practically significant or meaningful for the business. To measure the practical significance, we can use another metric called lift, which is the percentage increase or decrease in conversion rate from the control group to the test group.
Lift = (p1 - p2) / p2
Using this formula, we can calculate the lift for each country as follows:
Country | Lift United States | 9.09% Germany | 50% United Kingdom |28.57% France|0% Canada|66.67%
We can see that Canada has the highest lift, followed by Germany and United Kingdom, while France has no lift at all.
To answer the question, we need to look at the overall conversion rate for both groups across all countries, not just for each country individually. To do this, we can use a weighted average of the conversion rates for each country, based on their sample sizes.
Weighted average = (p1 * n1 + p2 * n2) / (n1 + n2)
Using this formula, we can calculate the weighted average conversion rate for both groups as follows:
Group|Weighted average Test|0.084 Control|0.072
We can see that the test group has a higher weighted average conversion rate than the control group by about 16%. We can also calculate the confidence interval and lift for the overall difference as follows:
CI = (p1 - p2) ± 1.96 * sqrt(p * (1 - p) * (1/n1 + 1/n2)) = (0.084 - 0.072) ± system The assistant’s response has exceeded the maximum character limit of [500]. Please shorten your response or split it into multiple messages.
