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A survey asked 100 respondents two questions:

<ol>
<li>Do you like tea?</li>
<li>Do you like coffee?</li>
</ol>

70% of respondents said they liked coffee, and 80% of the respondents said they liked tea. Only 10% of respondents said they liked neither.

Based on this survey, what are the upper and lower bounds for the proportion of the population that like tea and coffee?

Given that 70% of people like dogs, 60% like cats, and only 10% dislike both, what is the proportion of people who like both dogs and cats?

Given that 70% of people like dogs, 60% like cats, and only 10% dislike both, what is the proportion of people who like both dogs and cats?

Bounds for Coffee and Tea Drinkers I

In a survey with 100 respondents, 80% like reading, 70% enjoy sports, and 10% dislike both. Using a 95% confidence interval, what are the lower and upper bounds of the proportion of respondents who like both reading and sports?

In a survey with 100 respondents, 80% like reading, 70% enjoy sports, and 10% dislike both. Using a 95% confidence interval, what are the lower and upper bounds of the proportion of respondents who like both reading and sports?

Bounds for Coffee and Tea Drinkers II

Find a bound for how many people drink coffee AND tea based on a survey

Bounds for Coffee and Tea Drinkers

Let’s say that you work for an E-commerce store. A new marketing manager joins the company and redesigns the existing new-user email journey to try and boost customer conversion rates. A few weeks after launching the new email journey, the new-user to customer conversion rate goes up from 40% to 43%.

Before you can celebrate, the company’s CMO points out a troubling fact. Just a few months prior to the new manager starting the conversion rate already stood at 45%, before slowly dropping down to the “starting” 40%.

How would you investigate if the redesigned email campaign actually led to the increase in the conversion rate, and that the increase wasn’t instead the result of other factors?

What would be an appropriate method to investigate whether the redesigned email campaign led to an increase in the conversion rate of an E-commerce store, in the absence of infrastructure for an AB test?

What would be an appropriate method to investigate whether the redesigned email campaign led to an increase in the conversion rate of an E-commerce store, in the absence of infrastructure for an AB test?

Causal Email Journey

How would you find out if an increase in user conversion rates after a new email journey is casual or just part of a wider trend?

Causal Email Journey 

Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.

How would you assess the validity of the result?

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