A government sample survey plans to measure the LDL (bad) cholesterol level of a
ID: 3258394 • Letter: A
Question
A government sample survey plans to measure the LDL (bad) cholesterol level of an SRS of men aged 20 to 34. The researchers will report the mean x from their sample as an estimate of the mean LDL cholesterol level Au in this population. (a) Explain to someone who knows no statistics what it means to say that x is an "unbiased" estimator of u. O X is not systematically higher than or lower than A. x is systematically higher than or lower than Au (b) The sample result x is an unbiased estimator of the population truth no matter what size SRS the study uses. Explain to someone who knows no statistics why a large sample gives more trustworthy results than a small sample. o With large samples, x is more likely to be close to A, because with a larger sample comes more information (and therefore less uncertainty). O With large samples, x is more likely to be close to u, because with a larger sample comes less information (and therefore more uncertainty). O With large samples, x is more likely to be further away from u, because with a larger sample comes less information (and therefore more uncertainty). o With large samples, x is more likely to be further away from A, because with a larger sample comes more information (and therefore less uncertainty).Explanation / Answer
a) If we choose many samples, the average of the x -values from these samples will be close to µ.
so option b ) x^ is symetrically higher than or lower than µ.
b) option a ; that is, x^ is more likely to be close to the population truth. Also, x^ for a larger sample is less affected by outliers
because The larger sample will give more information, and therefore more precise results
c) no
because The central limit theorem says that the histogram of sample means (from many large samples) will look more and more Normal. and histogram sample values look like population disturtbtion
d) explain your answer
c &e
c)the central limit theorem says that the histogram of sample means (from many large samples) will look more and more Normal.
e) histogram sample values look like population disturtbtion what ever it might happen to be