Question

A water supplying company wishes to estimate the average amount that private customers pay per month....

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.

Homework Answers

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.

Hope this solution will help you to understand. If you are satisfied with the answer then please please give a like to this answer. Thank you.

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