Agenda of Week VII. Sampling Distribution Objective : Understanding the standard normal distribution Understanding the sampling distribution Week 6 1 Random.

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Presentation transcript:

Agenda of Week VII. Sampling Distribution Objective : Understanding the standard normal distribution Understanding the sampling distribution Week 6 1 Random variable Normal dist. Definition Properties Example Estimation Standard Normal Sampling Dist. 32 Definition Properties

Review of Week VI Objective : Understanding the random variable and probability Definition Probability Random variable 1 Definition Properties Normal distribution Normal Dist. 2

Standard Normal Distribution o A most useful modification of ND Eq. 7.4 Characteristics: Table 7.3 pdf. and cdf.: Figure 7.9

Sampling Distribution o So far, under the assumption that all parameters of population is known to us, the probability of a value has been calculated

Sampling Distribution o Definition When a population is normally distributed,, how is the means of samples from the population distributed? o N vs. n N: the number of obs. in population (Population size) n: the number of obs. in a sample (Sample size)

Sampling Distribution o Possible number of samples from a population Example: N=50, n=5 o Sampling variation Figure 8.1 and Table in the top of p.296

Sampling Distribution o When 100 samples of 10 obs. are drawn, their sample means and s.d. are expressed as: o r.v. is defined if it has one of and can be calculated

Sampling Distribution o In this case, r.v. is and Z for becomes Figure in p.298 o CLT for a mean P.299

Sampling Distribution o Example Height of female college students: Probability that sample mean is greater than 160 and less than 163 when drawing 100 students

Sampling Distribution

o Estimation or o Point estimation Estimation of only with a value of Weakness ???

Sampling Distribution o Interval estimation Significant level ( ) and critical value under a s.l. ( )

Sampling Distribution o Interval estimation Significant level ( ) and critical value under a s.l. ( )

Sampling Distribution o Interval estimation Significant level ( ) and critical value under a s.l. ( )