An industrial/organizational psychologist is consulting with Family Practice Pediatrics, which has just lost several of its best doctors to a rival pediatric practice. The management at Family Practice would like to know what it can do to increase job satisfaction for its remaining pediatricians. The psychologist is trying to determine whether significant information will be lost if she surveys a subset rather than every single pediatrician at Family Practice.
The following table lists the job satisfaction scores for all eight pediatricians at Family Practice as well as four examples of possible four-pediatrician samples. At the bottom of the table, the variance listed in the second column for all eight pediatricians is the population variance for the eight pediatricians (that is, sigma^2 = SS/N = SS/8). The variances listed in the third through the sixth columns are the sample variances for each of the four-pediatrician samples (that is, s^2 = SS/(n - 1) = SS/3).
Pediatrician Satisfaction Sample 1 Sample 2 Sample 3 Sample 4
A 5 x x x
B 6 x x x x
C 8 x x x
D 3 x
E 7 x x
F 2 x
G 8 x x
H 9
Mean 6.00 6.75 6.50 5.25 6.00
Variance 5.50 2.25 1.67 6.25 4.67
What is the mean of the four sample means?
What is the mean of the four sample variances?
A sample statistic is_______ if the average value of the sample statistic, obtained over all possible samples, is equal to the population parameter.
A sample statistic is_______ if it consistently underestimates or overestimates the corresponding population parameter.
A sample mean (that is, M = sigma X/n) is_________ estimator of the population mean. A sample variance that is computed as s^2 = SS/(n - 1) is estimator of the population variance.

Complete Question

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Answer:

What is the mean of the four sample means is  [tex]\= x  =  6.125 [/tex]

What is the mean of the four sample variances is   [tex]\= x_v  =  3.71[/tex]

A sample statistic is an unbiased  point estimator  if the average value of the sample statistic, obtained over all possible samples, is equal to the population parameter.

A sample statistic is biased if it consistently underestimates or overestimates the corresponding population parameter.

A sample mean (that is, M = sigma X/n) is unbiased estimator of the population mean

A sample variance that is computed as s^2 = SS/(n - 1) is unbiased estimator of the population variance.

Step-by-step explanation:

From the question we are told that

   Mean    6.00   6.75    6.50    5.25    6.00

   Variance    5.50    2.25    1.67   6.25  4.67

Generally the mean of the four sample means is mathematically represented as

      [tex]\= x  =  \frac{6.00+   6.75 +   6.50  +  5.25  +  6.00}{4}[/tex]

=>  [tex]\= x  =  6.125 [/tex]

Generally the mean of the four sample variances is mathematically represented as

      [tex]\= x_v  =  \frac{5.50+ 2.25+ 1.67+ 6.25 +4.67}{4}[/tex]

=>    [tex]\= x_v  =  3.71[/tex]

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