A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:
Question
A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:
Solution
The standard error of the sampling distribution of the sample proportion can be calculated using the formula:
SE = sqrt [ P(1 - P) / n ]
where: P is the population proportion, n is the sample size.
Given that P = 0.25 and n = 250, we can substitute these values into the formula:
SE = sqrt [ 0.25(1 - 0.25) / 250 ] SE = sqrt [ 0.25 * 0.75 / 250 ] SE = sqrt [ 0.1875 / 250 ] SE = sqrt [ 0.00075 ]
Therefore, the standard error of the sampling distribution of the sample proportion is approximately 0.0274.
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The sampling distribution of the sample proportion is the distribution of values of the sample proportion from all possible samples of size n drawn from a population. When a sample proportion is calculated, the population from which the sample comes is discrete. The variance of the sample proportion is equal to the variance of a binomial random variable divided by the sample size squared. The sampling distribution of the sample proportion is approximately normally distributed provided the population is normally distributed.
define Sampling Error in statistics
A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use t Distribution Table & z Distribution Table.)Required:a. Determine the standard error of the mean. (Round your answer to 3 decimal places.)c. Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)
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