Let's say my data is like this

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Subscription rate of Apple user is 3/7 = 42.8%

Subscription rate of Android user is 4/10 = 40.0%

Subscription rate in population is 11/24 = 45.8%

How can I formulate and test the hypothesis that subscription rate of Apple user is statistically different (or not) from Android users and different (or not) from the population ?

t-test and ANOVA are working for difference in mean, yet I am not sure how do we answer the question of "statistically different (or not)" for other custom formulas

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    $\begingroup$ "subscription rate of Apple user is statistically different (or not) from Android users" Pearson chi-square test or Fisher's exact test. "different (or not) from the population" it is meaningless. $\endgroup$ – user158565 Dec 18 '18 at 3:59
  • $\begingroup$ Thanks. Sorry for the amateur question : can you say why it's meaningless ? 1 sample t-test could compare the element of sample to the population right ? $\endgroup$ – Kenny Dec 18 '18 at 4:05
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    $\begingroup$ Because Apple users are part of your population. $\endgroup$ – user158565 Dec 18 '18 at 4:09

You essentially have two categorical data types in this case: Phone type and Subscribed(1/0). This qualifies as a case for the use of Chi-square test of independence. IF you have small sample sizes, you'd use Fisher's exact test.

Null hypothesis: Subscription is independent of phone type.

You will not be testing means or variances here since both variables are categoric in nature, we can only count number of occurences.


different (or not) from the population

you can test hypothesis for difference in sample mean and population mean using single sample t-test.


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