RESEARCH METHODOLOGY

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STATISTICAL TECHNIQUES AND TOOLS

SAMPLING DISTRIBUTION

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x?
A
Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days
B
Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day
C
Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day
D
Approximately normal with mean 5.5 days and standard deviation 2.6 days
E
Approximately normal with mean 5.5 days and standard deviation 0.26 day
Explanation: 

Detailed explanation-1: -For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean X= and standard deviation X=/√n, where n is the sample size.

Detailed explanation-2: -The Sampling Distribution of a Sample Mean Sample means are less variable than individual observations, because in any sample there will be high values and low values which tend to offset each other, keeping the mean or average near the population mean.

Detailed explanation-3: -The sample means do not vary as much as the individual values in the population. That the sample means are less variable than the individual values in the population follows directly from the fact that each sample mean averages together all the values in the sample.

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