# confidence interval

• Jul 30th 2007, 07:30 PM
mkcar
confidence interval
I'm so lost on how to do this problem,
could someone take me step by step on how to solve it pleeze.

the question is construct the indicated confidence interval for the population mean.
__
c= 0.95, x ( the line is supposed to be on top of the x)=31.39, s=0.8,n=82
if you could take me through the steps on how you do this I can maybe try to fiqure out how to do the next ones. Thank you
• Jul 30th 2007, 10:08 PM
CaptainBlack
Quote:

Originally Posted by mkcar
I'm so lost on how to do this problem,
could someone take me step by step on how to solve it pleeze.

the question is construct the indicated confidence interval for the population mean.
__
c= 0.95, x ( the line is supposed to be on top of the x)=31.39, s=0.8,n=82
if you could take me through the steps on how you do this I can maybe try to fiqure out how to do the next ones. Thank you

Suppose that $X$ is a normally distributed random variable, and we have a sample
$x_1, .., x_{82}$ of $X$'s, then the statistic:

$
t=\frac{\mu-\bar{x}}{s/\sqrt{n}}
$

has a t-distribution with $n-1$ degrees of freedom, and so looking this up in a
table of the t-distribution we find that a 95% interval for $t$ with 81 degrees of
freedom is $(-1.99, 1.99)$, so th corresponding interval for the population mean $\mu$ is:

$
( \bar{x}-1.99 ~s/\sqrt{n},\bar{x}+1.99 ~s/\sqrt{n})
$

Now plug in your numerical values and its done.

RonL
{"extraction_info": {"found_math": true, "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": 9, "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": 0.9091241359710693, "perplexity": 365.77686579832533}, "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-2017-51/segments/1512948597295.74/warc/CC-MAIN-20171217171653-20171217193653-00420.warc.gz"}