A plan to sample 2500 adults nationwide regarding their use

A plan to sample 2500 adults nationwide regarding their use of ATMs by simple random sampling of telephone numbers is cut down, due to limited expenses, to 2500 adults in the state of California. The results are input to a computer to construct a 95% confidence interval of the national population mean. Will the estimate be good? Explain.

Solution

Any sample will be considered to be good to estimate the concerned population parameter if its covers all aspects of the data thus covering all possible variation without any bias.

Therefore, if we want a good estimate for nation wide population mean then it would be advisable to sample collect a random sample from whole a population instead of drawing a sample from particular region.

Such as, here if we collect the sample only from the state of California then it wont be good to estimate the national population mean from it because the data from one state may not represent the characteristics of whole of population and thus the result based on one particular region is more likley to be biased one.

Thus it wont be good estimate.