[amp_mcq option1=”If a population from which a sample is drawn is normally distributed the sampling distribution of mean (SDM) will be normal for all sample sizes” option2=”The mean of the SDM is the population mean” option3=”If the population is not normal from which the sample is drawn, the SDM is not normal for any sample size” option4=”If the population is not normal from which a sample is drawn, the SDM approaches normality as the sample size increases” correct=”option3″]<\/p>\n
The correct answer is: C. If the population is not normal from which the sample is drawn, the SDM is not normal for any sample size.<\/p>\n
The Central Limit Theorem (CLT) states that, given a sufficiently large sample size, the sampling distribution of the mean of a variable will be approximately normally distributed, regardless of the distribution of the variable in the population. This means that, even if the population is not normally distributed, the sample mean will be approximately normally distributed if the sample size is large enough.<\/p>\n
The CLT is a powerful tool that can be used to make inferences about a population based on a sample. However, it is important to note that the CLT only applies to the sampling distribution of the mean. The CLT does not apply to the sampling distribution of other statistics, such as the median or the mode.<\/p>\n
In addition, the CLT only applies to sufficiently large sample sizes. The exact sample size required for the CLT to apply depends on the distribution of the variable in the population. For example, if the population is normally distributed, the CLT will apply with a sample size of 30 or more. However, if the population is not normally distributed, a larger sample size may be required for the CLT to apply.<\/p>\n
Overall, the CLT is a powerful tool that can be used to make inferences about a population based on a sample. However, it is important to note that the CLT only applies to the sampling distribution of the mean, and that the CLT only applies to sufficiently large sample sizes.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”If a population from which a sample is drawn is normally distributed the sampling distribution of mean (SDM) will be normal for all sample sizes” option2=”The mean of the SDM is the population mean” option3=”If the population is not normal from which the sample is drawn, the SDM is not normal for any sample … <\/p>\n