If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
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A recent survey of 50 executives who were laid off from their previous position revealed it took a mean of 26 weeks for them to find anoher positio. the standard deviation of the sample was 6.2 weeks. construct a 95 % confidence interval for the population. Is it reasonable that the population mean is 28 weeks? Justify your answer
a) T or F The sampling distribution will be normal. Explain your answer. b) Find the mean and standard deviation of the sampling distribution. c) We pick one of our samples from the sampling distribution what is the probability that this sample has a mean that is greater than 109 ? Is this a usual or unusual event? these are the rest of the question.
The standard error of the mean and sampling error are two similar but still very different things. In order to find some statistical information about a group that is extremely large, you are often only able to look into a small group called a sample. In order to gain some insight into the reliability of your sample, you have to look at its standard deviation. Standard deviation in general tells you spread out or variable your data is. If you have a low standard deviation, that means your data is very close together with little variability. The standard deviation of the mean is calculated by dividing the standard deviation of the sample by the square root of the number of things in the sample. What this essentially tells you is how certain are that your sample accurately describes the entire group. A low standard error of the mean implies a very high accuracy. While the standard error of the mean just gives a sense for how far you are away from a true value, the sampling error gives you the exact value of the error by subtracting the value calculated for the sample from the value for the entire group. However, since it is often hard to find a value for an entire large group, this exact calculation is often impossible, while the standard error of the mean can always be found.
You are studying the sample because you want to find out information about the whole population. If the sample you have drawn from the population does not represent the population, you will find out about the sample but will not find out about the population.