Statistics
Topics

# One-sample t test

## Key Questions

• Conditions for conducting one-sample t-test for mean:
1.) Parent population from which the sample is drawn should be normal.
2.) The sample observations are independent. i.e the given sample is random.
3.) The ''population'' standard deviation is unknown.

• t-distribution is also known as student's t-distribution .....

this is a probability distribution that is used to estimate the population parameter when the given sample space is small or when the variance is unknown .

this type of distribution has three types of properties and they are:

• mean distribution is equal to zero

• variance is equal to v/ (v-2) where the v is the degrees of freedom and v is always less than 2

- the variance is always greater than one. with infinite degrees of freedom the t-distribution is same as standard normal distribution.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9900897741317749, "perplexity": 686.0674439684467}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827769.75/warc/CC-MAIN-20181216143418-20181216165418-00305.warc.gz"}