1. As the sample size increases, the mean of sampling errors (of the mean) acros

Question

1. As the sample size increases, the mean of sampling errors (of the mean) across all random samples drawn from the same population will decrease. True or False? Why?
2. The variability of sampling errors (of the mean) is larger than the variability of sample means. True or False Why?
3. A 90% condence interval covers the sample mean in 90% random samples drawn fromthe same population. True or False? Why?
4. A condence interval for the mean is calculated by adding and subtracting a value toand from the population mean. True or False? Why?

Explanation / Answer

1) THIS STATEMENT IS TRUE BECAUSE THE SAMPLING ERROR IS INVERSELY PROPORTIONAL TO THE SAMPLE SIZE AND WHEN THE SIZE INCREASES THE ERROR DECREASES.

2) THE VARIABLILITY OF ERROR IS INVERSELY PROPORTIONAL TO SQRT(SIZE) WHERE AS THE VARIABLILITY OF MEAN IS INVERSELY PROPORTION T SIZE. THEREFORE MORE THE SIZE THE SAMPLING ERROR WILL STILL BE LARGE. HENCE TRUE.

3) NO FALSE AS THE CONFIDENCE INTERVAL COVER ALL THE SAMPLE OF THE DATA IT MEANS THAT THE CHANCE OF MEAN TO BE IN THE INTERVAL IS 90%

4) THIS IS TRUE BECAUSE THE CONFIDENCE INTERVAL IS CALCULATED BY ADDING AND SUBTRACTING THE MARGIN OF ERROR FROM THE MEAN.

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