Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

question 29

Essay

Solve the problem.
-Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later.
The numbers of people in the households are 1, 4, and 8. Consider the values of 1, 4, and 8 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 8.
The nine different samples are as follows: (1, 1), (1, 4), (1, 8), (4, 1), (4, 4), (4, 8), (8, 1), (8, 4), and (8, 8). (i) Find
the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard
deviations in the format of a table representing the probability distribution. (ii) Compare the population
standard deviation to the mean of the sample standard deviations. (iii) Do the sample standard deviations
target the value of the population standard deviation? In general, do standard deviations make good estimators
of population standard deviation? Why or why not?

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Definitions:

Gestalt Therapy

An approach in mental health counseling that underlines personal accountability and zeroes in on the present moment experiences of the person seeking help, the rapport between therapist and client, the influence of social and environmental factors on an individual's life, and the personal modifications made in response to their broader context.

Emotional Flooding Therapies

Therapeutic techniques designed to expose individuals to a large amount of emotional stimuli with the goal of processing and overcoming intense emotions or traumas.

Authentic Contact

Authentic contact refers to engaging with another individual in a genuine, transparent, and sincere manner, fostering real connection and understanding.

Safe Emergencies

Scenarios or exercises designed to simulate emergency situations in a controlled, safe environment, often for the purpose of training or preparedness.