Chap6A - STATISTICS 211 HONORS Chapter 6A STATISTICAL...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
STATISTICS 211 HONORS PROF EMANUEL PARZEN Chapter 6A STATISTICAL INFERENCE CONFIDENCE INTERVALS HYPOTHESIS TESTS STATISTICAL INFERENCE seeks to learn from data values of parameters of the probability distribution obeyed by the random variable of which the data is a random sample. It is important to remember that one learns from a random sample ONLY about the population represented in the sample. POINT ESTIMATOR OF A PARAMETER: Learning starts with a point estimator of the parameter and an exact or approximate knowledge of the sampling distribution of the estimator given the parameter value. To answer Scientific questions we prefer interval estimators of the parameter (called confidence intervals) which provide information about the parameter (including precision (margins of error, error bars)) that fit the observed data. Formulas for statistic inference have a general theory but it is important to learn each parameter its own details which are important in practice. CONTINUOUS DATA SUMMARY: For a continuous or quantitative random variable Y a sample has summary Y name of variable Sample size sample mean standard deviation SE(mean) n M(Y) Sobserv, Sassume S/sqrt(n) QUANTILE SUMMARY: Quantiles MIN Q1 Q2 Q3 MAX, boxplot, and QQ plot of continuous data are increasingly being reported and diagnosed to identify probability distribution (especially Normal) to fit to data In this chapter we do not emphasize reporting and interpreting the quantile summary of continuous data. EXAMPLE: Y fill weight (in ounces) of box or can produced by a plant n mean M(Y) Sobserv SE(mean) 100 12.1 . 1 .1/10=.01 CONFIDENCE INTERVAL ENDPOINT FUNCTION: For large samples confidence interval endpoint function, denoted \mu(P)=Q(P;\mu), is given approximately by (applying Central Limit Theorem) \mu(P)=M(Y)+Q(P;Z) S/sqrt(n) It is derived from pivot Z(M(Y),\mu) defined below under hypothesis test. Note that for n<40 and Y is assumed to obey Normal distribution, confidence interval endpoint function of parameter \mu is exactly (and more accurately) mu(P)=M(Y)+Q(P;Student(n-1)) S/sqrt(n
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Confidence interval of confidence level 1-\alpha is an interval of values of \mu with endpoints \mu(lower limit)=\mu(\alpha/2) \mu(upper limit)=\mu(1-\alpha/2)) EXAMPLE: For Y fill weight of box, with sample statistics summarized above, 90% confidence interval has endpoints, using Q(.05;Z)=-1.645, Q(.95;Z)=1.645, \mu(.05)=12.1 – 1.645 (.01)= 12.08355, \mu(.95)=12.1+1.645 (.01)=12.11645 HYPOTHESIS TEST: Formulas for confidence intervals are derived by finding a pivot which is a function of estimator and parameter whose distribution does not depend on the parameter. For sample mean M(Y)
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern