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Let's say my data is like this

enter image description here

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
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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.

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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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