Hypothesis Tests in Inference

[ukr-reader]

Can two additional tests be included in the Inference app as these are studied by all A-level students in the UK.

Correlation - hypotheses of the form H_0: \rho=0; H_1: \rho>0 (or < 0, or \neq 0), sample size n. Calculator should provide the critical value calculated using \sqrt{{x^2}/{x^2+n-2}} where x=invt(\alpha,n-2). Even better if it can include the p value as well. Graphical illustration can be a horizontal rectangle with a scale from -1 to 1. Critical region shaded grey etc like in other tests.

One proportion - we don't teach the z-test - just working directly with a binomial distribution. Calculator should provide the p value. Even better if it can include the critical region. Graphical illustration can be a binomial distribution with similar shading to other tests.

Happy to provide more clarification if needed

[adri1numworks]

Hi!

Could you precise which correlation test you're introducing here? Are you referring to the Pearson method?

Also, could you develop on why the One proportion t-test currently available in the Inference app does not suit your need? I'm not sure I understand the difference with what you propose.

Thank you very much!

[ukr-reader]

Yes, the correlation test is the Pearson product moment correlation coefficient test for zero correlation:

For the Binomial one proportion test, I don't actually know what a t-test is sorry. I'm aware of a z-test that uses a Normal approximation of the binomial distribution. Maybe that's the same thing by a different name. But what we have to teach is like this example:

Method 2 (not shown) is finding the critical region within that binomial distribution.

[Image credits: Pearson Edexcel A Level Maths Textbooks]