Question

A water supplying company wishes to estimate the average amount that private customers pay per month. A random sample of 25  customers' bills during a given month produced a sample mean of $30, and a sample standard deviation of $5. (So, the current problem differs from the previous. In the previous problem, $5 presented the standard deviation for the whole population, while in these problem, $5 is the standard deviation on; only for a sample of 25 customers.)  

a) Without any calculations, do you expect that the 90% confidence interval in the case of the current problem will be wider than that in the previous problem or narrower?  Justify the answer.

Answer 1

Yes, the 90% confidence interval in this case of the current problem will be wider than that in the previous problem.

The critical value for this problem is t_{​​​​​​0.05;24} = 1.711 and for previous problem the critical value is Z_{​​​​​​0.05} = 1.645.

Also, the sample size is smaller for this problem than the previous one.

So, that is why without doing any calculations we can conclude that the 90% confidence interval in this case of the current problem will be wider than that in the previous problem.

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