External materials

Useful links and materials

Tables and CDF calculation tools

Table for the standard normal distribution values: 🔮.
Tables for the Student’s t-distribution values: ➡, and ➡.
Calculator of the t-score: 💻.

Recommended external information sources

MIT brief but well-written review on joint distributions
Nice introductory coverage of confidence intervals

Note that in the subtopic “Comparing Two Means” there is given the most complicated case, when we do not know variances \(\sigma_1^2\) and \(\sigma_2^2\) of two populations, moreover they may not be equal to each other. We didn’t cover this case, and it’s better here to follow our materials.
Nice introductory coverage of hypothesis testing, which can help you to look at the HT from slightly another position of the different author. Please, also note here, that there is not full coverage of the subtopic “Tests on Differences of Population Means”. It is better here, as well, to follow our materials.
You can find interesting articles on the website statisticsbyjim.com. Among others I can recommend one graphically representing \(\alpha\) and \(p\)-values, article about how hypothesis testing works in general, and the article devoted to significance levels.

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# Useful links and materials

## Tables and CDF calculation tools

1. Table for the standard normal distribution values: [🔮](http://statcalculators.com/z-score-table-standard-normal-distribution/).
2. Tables for the Student's t-distribution values: [➡](https://www.statology.org/how-to-read-t-distribution-table/), and [➡](https://www.tdistributiontable.com/).
3. Calculator of the t-score: [💻](https://stattrek.com/online-calculator/t-distribution.aspx).

## Recommended external information sources

1. [MIT brief but well-written review on joint distributions](https://math.mit.edu/~dav/05.dir/class7-prep-a.pdf)

2. [Nice introductory coverage of confidence intervals](/documents/Confidence_Intervals_external_material.pdf)

    Note that in the subtopic "Comparing Two Means" there is given the most complicated case, when we do not know variances $\sigma_1^2$ and $\sigma_2^2$ of two populations, moreover they may not be equal to each other. We didn't cover this case, and it's better here to follow our materials.

3. [Nice introductory coverage of hypothesis testing](/documents/Hypothesis_Testing_external_material.pdf), which can help you to look at the HT from slightly another position of the different author.
    Please, also note here, that there is not full coverage of the subtopic "Tests on Differences of Population Means". It is better here, as well, to follow our materials.
    
4. You can find interesting articles on the website [statisticsbyjim.com](https://statisticsbyjim.com/). Among others I can recommend [one](https://statisticsbyjim.com/hypothesis-testing/hypothesis-tests-significance-levels-alpha-p-values/) graphically representing $\alpha$ and $p$-values, [article](https://statisticsbyjim.com/hypothesis-testing/statistical-hypothesis-testing-overview/) about how hypothesis testing works in general, and the [article](https://statisticsbyjim.com/hypothesis-testing/significance-levels/) devoted to significance levels.