What in meant when we say that the sample meant \"Larget\" the population mean,

Question

What in meant when we say that the sample meant "Larget" the population mean, or that the sample mean in an estimator of the population mean? USA Today provided a "snapshot" illustrating poll results from 21, 944 subjects. The illustration showed that 43% answered "yes" to this question: "Would you rather have a boring job than no job?" The of error was given as plusminus 1 percentage point. (a) What important of the poll was not ?(At least, not here.) What would this piece of information tell you about the result? (b) Explain what is meant by the statement that "the margin of error is plusminus 1 parentage point." Given specific sample data, such as the data given in Exercise 1, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider? Suppose a simple random sample of community college students found a 95% confidence interval for the mean number of college credits to be (12.289, 12.991). (a) Translate the confidence interval into English. (b) Suppose you advisor tells you that a community college student takes 12 credits on average you think of her claim (hypothesis)

Explanation / Answer

population mean is parameter

sample mean is statistics

parameters are unknown , so we wish to estimate it .

Statistic is used to estimate parameter.

now we wish to find population mean , so we collect sample X1,X2 , .. Xn

sample mean is found.

Consider the random variables X1, X2, ..., Xn as a random sample from a population with mean µ. The average value of these observations is the sample mean. The sample mean is a random variable that is an estimator of the population mean. The expected value of the sample mean is equal to the population mean µ. Therefore, the sample mean is an unbiased estimator of the population mean.

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