Statistics and Confidence IntervalsConstruct a Confidence Interval of $95%$Confidence level of random sample from continuous distributionConfidence interval - No sampleInterval estimate to infer the population mean with a 95% confidence levelConfidence IntervalsConfidence Intervals Calculation and InterpretationConfidence intervals and significance testsHow to determine a confidence interval without knowing mean and varianceReducing the confidence interval with T distribitionConfidence Intervals using Pivotal Quantities

dbcc cleantable batch size explanation

Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?

Replacing matching entries in one column of a file by another column from a different file

Is it legal for company to use my work email to pretend I still work there?

Can a Cauchy sequence converge for one metric while not converging for another?

Today is the Center

Can a monk's single staff be considered dual wielded, as per the Dual Wielder feat?

Why do I get two different answers for this counting problem?

I'm flying to France today and my passport expires in less than 2 months

NMaximize is not converging to a solution

Are the number of citations and number of published articles the most important criteria for a tenure promotion?

Revoked SSL certificate

Do I have a twin with permutated remainders?

Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?

Arrow those variables!

Roll the carpet

Approximately how much travel time was saved by the opening of the Suez Canal in 1869?

What's the point of deactivating Num Lock on login screens?

Why doesn't Newton's third law mean a person bounces back to where they started when they hit the ground?

What typically incentivizes a professor to change jobs to a lower ranking university?

Maximum likelihood parameters deviate from posterior distributions

LaTeX: Why are digits allowed in environments, but forbidden in commands?

Unable to deploy metadata from Partner Developer scratch org because of extra fields

What defenses are there against being summoned by the Gate spell?



Statistics and Confidence Intervals


Construct a Confidence Interval of $95%$Confidence level of random sample from continuous distributionConfidence interval - No sampleInterval estimate to infer the population mean with a 95% confidence levelConfidence IntervalsConfidence Intervals Calculation and InterpretationConfidence intervals and significance testsHow to determine a confidence interval without knowing mean and varianceReducing the confidence interval with T distribitionConfidence Intervals using Pivotal Quantities













0












$begingroup$


Given the following set of values:



10,11,14,95,73,30,29,9,97,94,70



How do I calculate a 99% confidence interval for the sample mean? I am assuming that the variance is 10



Well, the idea I have is to assume that the distribution is normal, but after that i'm not completely sure what to do next. In particular, I am unable to find the z-score that corresponds to the z-score in the formula for the CI, i'm not sure what to input in R to find the CI. The formula for the confidence interval is:



$x-z_fraca2 fracsigma^2sqrt(n)$ and $x+z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean. Here the significance level (a) is 0.01.










share|cite|improve this question











$endgroup$











  • $begingroup$
    What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
    $endgroup$
    – Brian
    Mar 21 at 17:56










  • $begingroup$
    Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
    $endgroup$
    – topologicalmagician
    Mar 21 at 17:57










  • $begingroup$
    Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
    $endgroup$
    – Brian
    Mar 21 at 18:00











  • $begingroup$
    @Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
    $endgroup$
    – topologicalmagician
    Mar 21 at 18:04
















0












$begingroup$


Given the following set of values:



10,11,14,95,73,30,29,9,97,94,70



How do I calculate a 99% confidence interval for the sample mean? I am assuming that the variance is 10



Well, the idea I have is to assume that the distribution is normal, but after that i'm not completely sure what to do next. In particular, I am unable to find the z-score that corresponds to the z-score in the formula for the CI, i'm not sure what to input in R to find the CI. The formula for the confidence interval is:



$x-z_fraca2 fracsigma^2sqrt(n)$ and $x+z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean. Here the significance level (a) is 0.01.










share|cite|improve this question











$endgroup$











  • $begingroup$
    What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
    $endgroup$
    – Brian
    Mar 21 at 17:56










  • $begingroup$
    Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
    $endgroup$
    – topologicalmagician
    Mar 21 at 17:57










  • $begingroup$
    Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
    $endgroup$
    – Brian
    Mar 21 at 18:00











  • $begingroup$
    @Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
    $endgroup$
    – topologicalmagician
    Mar 21 at 18:04














0












0








0





$begingroup$


Given the following set of values:



10,11,14,95,73,30,29,9,97,94,70



How do I calculate a 99% confidence interval for the sample mean? I am assuming that the variance is 10



Well, the idea I have is to assume that the distribution is normal, but after that i'm not completely sure what to do next. In particular, I am unable to find the z-score that corresponds to the z-score in the formula for the CI, i'm not sure what to input in R to find the CI. The formula for the confidence interval is:



$x-z_fraca2 fracsigma^2sqrt(n)$ and $x+z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean. Here the significance level (a) is 0.01.










share|cite|improve this question











$endgroup$




Given the following set of values:



10,11,14,95,73,30,29,9,97,94,70



How do I calculate a 99% confidence interval for the sample mean? I am assuming that the variance is 10



Well, the idea I have is to assume that the distribution is normal, but after that i'm not completely sure what to do next. In particular, I am unable to find the z-score that corresponds to the z-score in the formula for the CI, i'm not sure what to input in R to find the CI. The formula for the confidence interval is:



$x-z_fraca2 fracsigma^2sqrt(n)$ and $x+z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean. Here the significance level (a) is 0.01.







statistics probability-distributions normal-distribution statistical-inference






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 21 at 18:11







topologicalmagician

















asked Mar 21 at 17:50









topologicalmagiciantopologicalmagician

1199




1199











  • $begingroup$
    What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
    $endgroup$
    – Brian
    Mar 21 at 17:56










  • $begingroup$
    Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
    $endgroup$
    – topologicalmagician
    Mar 21 at 17:57










  • $begingroup$
    Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
    $endgroup$
    – Brian
    Mar 21 at 18:00











  • $begingroup$
    @Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
    $endgroup$
    – topologicalmagician
    Mar 21 at 18:04

















  • $begingroup$
    What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
    $endgroup$
    – Brian
    Mar 21 at 17:56










  • $begingroup$
    Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
    $endgroup$
    – topologicalmagician
    Mar 21 at 17:57










  • $begingroup$
    Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
    $endgroup$
    – Brian
    Mar 21 at 18:00











  • $begingroup$
    @Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
    $endgroup$
    – topologicalmagician
    Mar 21 at 18:04
















$begingroup$
What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
$endgroup$
– Brian
Mar 21 at 17:56




$begingroup$
What are your thoughts? Are you familiar with any formulas that concern confidence intervals? What computations can you do?
$endgroup$
– Brian
Mar 21 at 17:56












$begingroup$
Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
$endgroup$
– topologicalmagician
Mar 21 at 17:57




$begingroup$
Well, I know the formula for the confidence interval, but i'm not sure how to find the z-score, I know that I can use R, but i'm not sure what to write in R.
$endgroup$
– topologicalmagician
Mar 21 at 17:57












$begingroup$
Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
$endgroup$
– Brian
Mar 21 at 18:00





$begingroup$
Do you know what the "99%" in the confidence interval means? Can you relate this to the Normal distribution in some way? Do you know how z-scores relate to the Normal distribution?
$endgroup$
– Brian
Mar 21 at 18:00













$begingroup$
@Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
$endgroup$
– topologicalmagician
Mar 21 at 18:04





$begingroup$
@Brian Yes, a CI is the 100(1-a)% interval in which the true parameter lies in, a is the significance level. The formula for the CI is : $x+z_fraca2 fracsigma^2sqrt(n)$ and : $x-z_fraca2 fracsigma^2sqrt(n)$ where x denotes the mean
$endgroup$
– topologicalmagician
Mar 21 at 18:04











1 Answer
1






active

oldest

votes


















1












$begingroup$

It is likely that you are asked to find a confidence interval for the (unknown) population mean, not the sample mean. The sample mean is not a parameter of interest, it can be calculated from the sample.



A conventional setup for the problem is that you have a sample $mathbf X=(X_1,X_2,ldots,X_n)$ of size $n=11$ from a $N(mu,sigma_0^2)$ population (by assumption) with $sigma_0^2=10$. You have to find a confidence interval for the mean $mu$.



A suitable pivotal quantity here is $$Q(mathbf X,mu)=fracsqrtn(overline X-mu)sigma_0sim N(0,1)$$



, where $overline X=frac1nsumlimits_i=1^n X_i$ is the sample mean.



So if $z_alpha/2$ be such that $P(Z>z_alpha/2)=alpha/2$ where $Zsim N(0,1)$, you have $$P_mu(-z_alpha/2le Qle z_alpha/2)=1-alphaquad,forall,mu$$



You have to use the above to arrive at the form $$P_mu(c_1,le mule,, c_2)=1-alphaquad,forall,mu$$



A $100(1-alpha)%$ confidence interval for $mu$ is then $[c_1,c_2]$.






share|cite|improve this answer











$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function ()
    return StackExchange.using("mathjaxEditing", function ()
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    );
    );
    , "mathjax-editing");

    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "69"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader:
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    ,
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );













    draft saved

    draft discarded


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157138%2fstatistics-and-confidence-intervals%23new-answer', 'question_page');

    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    It is likely that you are asked to find a confidence interval for the (unknown) population mean, not the sample mean. The sample mean is not a parameter of interest, it can be calculated from the sample.



    A conventional setup for the problem is that you have a sample $mathbf X=(X_1,X_2,ldots,X_n)$ of size $n=11$ from a $N(mu,sigma_0^2)$ population (by assumption) with $sigma_0^2=10$. You have to find a confidence interval for the mean $mu$.



    A suitable pivotal quantity here is $$Q(mathbf X,mu)=fracsqrtn(overline X-mu)sigma_0sim N(0,1)$$



    , where $overline X=frac1nsumlimits_i=1^n X_i$ is the sample mean.



    So if $z_alpha/2$ be such that $P(Z>z_alpha/2)=alpha/2$ where $Zsim N(0,1)$, you have $$P_mu(-z_alpha/2le Qle z_alpha/2)=1-alphaquad,forall,mu$$



    You have to use the above to arrive at the form $$P_mu(c_1,le mule,, c_2)=1-alphaquad,forall,mu$$



    A $100(1-alpha)%$ confidence interval for $mu$ is then $[c_1,c_2]$.






    share|cite|improve this answer











    $endgroup$

















      1












      $begingroup$

      It is likely that you are asked to find a confidence interval for the (unknown) population mean, not the sample mean. The sample mean is not a parameter of interest, it can be calculated from the sample.



      A conventional setup for the problem is that you have a sample $mathbf X=(X_1,X_2,ldots,X_n)$ of size $n=11$ from a $N(mu,sigma_0^2)$ population (by assumption) with $sigma_0^2=10$. You have to find a confidence interval for the mean $mu$.



      A suitable pivotal quantity here is $$Q(mathbf X,mu)=fracsqrtn(overline X-mu)sigma_0sim N(0,1)$$



      , where $overline X=frac1nsumlimits_i=1^n X_i$ is the sample mean.



      So if $z_alpha/2$ be such that $P(Z>z_alpha/2)=alpha/2$ where $Zsim N(0,1)$, you have $$P_mu(-z_alpha/2le Qle z_alpha/2)=1-alphaquad,forall,mu$$



      You have to use the above to arrive at the form $$P_mu(c_1,le mule,, c_2)=1-alphaquad,forall,mu$$



      A $100(1-alpha)%$ confidence interval for $mu$ is then $[c_1,c_2]$.






      share|cite|improve this answer











      $endgroup$















        1












        1








        1





        $begingroup$

        It is likely that you are asked to find a confidence interval for the (unknown) population mean, not the sample mean. The sample mean is not a parameter of interest, it can be calculated from the sample.



        A conventional setup for the problem is that you have a sample $mathbf X=(X_1,X_2,ldots,X_n)$ of size $n=11$ from a $N(mu,sigma_0^2)$ population (by assumption) with $sigma_0^2=10$. You have to find a confidence interval for the mean $mu$.



        A suitable pivotal quantity here is $$Q(mathbf X,mu)=fracsqrtn(overline X-mu)sigma_0sim N(0,1)$$



        , where $overline X=frac1nsumlimits_i=1^n X_i$ is the sample mean.



        So if $z_alpha/2$ be such that $P(Z>z_alpha/2)=alpha/2$ where $Zsim N(0,1)$, you have $$P_mu(-z_alpha/2le Qle z_alpha/2)=1-alphaquad,forall,mu$$



        You have to use the above to arrive at the form $$P_mu(c_1,le mule,, c_2)=1-alphaquad,forall,mu$$



        A $100(1-alpha)%$ confidence interval for $mu$ is then $[c_1,c_2]$.






        share|cite|improve this answer











        $endgroup$



        It is likely that you are asked to find a confidence interval for the (unknown) population mean, not the sample mean. The sample mean is not a parameter of interest, it can be calculated from the sample.



        A conventional setup for the problem is that you have a sample $mathbf X=(X_1,X_2,ldots,X_n)$ of size $n=11$ from a $N(mu,sigma_0^2)$ population (by assumption) with $sigma_0^2=10$. You have to find a confidence interval for the mean $mu$.



        A suitable pivotal quantity here is $$Q(mathbf X,mu)=fracsqrtn(overline X-mu)sigma_0sim N(0,1)$$



        , where $overline X=frac1nsumlimits_i=1^n X_i$ is the sample mean.



        So if $z_alpha/2$ be such that $P(Z>z_alpha/2)=alpha/2$ where $Zsim N(0,1)$, you have $$P_mu(-z_alpha/2le Qle z_alpha/2)=1-alphaquad,forall,mu$$



        You have to use the above to arrive at the form $$P_mu(c_1,le mule,, c_2)=1-alphaquad,forall,mu$$



        A $100(1-alpha)%$ confidence interval for $mu$ is then $[c_1,c_2]$.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Mar 21 at 19:07

























        answered Mar 21 at 18:56









        StubbornAtomStubbornAtom

        6,29831440




        6,29831440



























            draft saved

            draft discarded
















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid


            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.

            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157138%2fstatistics-and-confidence-intervals%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            Popular posts from this blog

            Solar Wings Breeze Design and development Specifications (Breeze) References Navigation menu1368-485X"Hang glider: Breeze (Solar Wings)"e

            Kathakali Contents Etymology and nomenclature History Repertoire Songs and musical instruments Traditional plays Styles: Sampradayam Training centers and awards Relationship to other dance forms See also Notes References External links Navigation menueThe Illustrated Encyclopedia of Hinduism: A-MSouth Asian Folklore: An EncyclopediaRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to Play10.1353/atj.2005.0004The Illustrated Encyclopedia of Hinduism: A-MEncyclopedia of HinduismKathakali Dance-drama: Where Gods and Demons Come to PlaySonic Liturgy: Ritual and Music in Hindu Tradition"The Mirror of Gesture"Kathakali Dance-drama: Where Gods and Demons Come to Play"Kathakali"Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceMedieval Indian Literature: An AnthologyThe Oxford Companion to Indian TheatreSouth Asian Folklore: An Encyclopedia : Afghanistan, Bangladesh, India, Nepal, Pakistan, Sri LankaThe Rise of Performance Studies: Rethinking Richard Schechner's Broad SpectrumIndian Theatre: Traditions of PerformanceModern Asian Theatre and Performance 1900-2000Critical Theory and PerformanceBetween Theater and AnthropologyKathakali603847011Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceBetween Theater and AnthropologyBetween Theater and AnthropologyNambeesan Smaraka AwardsArchivedThe Cambridge Guide to TheatreRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeThe Garland Encyclopedia of World Music: South Asia : the Indian subcontinentThe Ethos of Noh: Actors and Their Art10.2307/1145740By Means of Performance: Intercultural Studies of Theatre and Ritual10.1017/s204912550000100xReconceiving the Renaissance: A Critical ReaderPerformance TheoryListening to Theatre: The Aural Dimension of Beijing Opera10.2307/1146013Kathakali: The Art of the Non-WorldlyOn KathakaliKathakali, the dance theatreThe Kathakali Complex: Performance & StructureKathakali Dance-Drama: Where Gods and Demons Come to Play10.1093/obo/9780195399318-0071Drama and Ritual of Early Hinduism"In the Shadow of Hollywood Orientalism: Authentic East Indian Dancing"10.1080/08949460490274013Sanskrit Play Production in Ancient IndiaIndian Music: History and StructureBharata, the Nāṭyaśāstra233639306Table of Contents2238067286469807Dance In Indian Painting10.2307/32047833204783Kathakali Dance-Theatre: A Visual Narrative of Sacred Indian MimeIndian Classical Dance: The Renaissance and BeyondKathakali: an indigenous art-form of Keralaeee

            Urgehal History Discography Band members References External links Navigation menu"Mediateket: Urgehal""Interview with Enzifer of Urgehal, 2007""Urgehal - Interview"Urgehal"Urgehal Frontman Trondr Nefas Dies at 35"Urgehal9042691cb161873230(data)0000 0001 0669 4224no2016126817ee6ccef6-e558-44b6-b059-dbbb5b913b24145036459145036459