A sample of 64 resistors are taken from a production line and are found to have

Question

A sample of 64 resistors are taken from a production line and are found to have a sample mean of 998 Ohms. The population distribution for the resistances is unknown but the population standard deviation is known to be 10 Ohms. (a) Find a 97% confidence interval for the population mean. (b) Answer the following two questions by writing either "narrower" or "wider" in the blank space. 1)If the sample size were increased to n = 1000 then the confidence interval would be than the confidence interval computed from a sample with n = 64. 2)A 99% confidence interval is than a 97% confidence interval.

Explanation / Answer

(a) Find a 97% confidence interval for the population mean.

Given a=0.03, |Z(0.015)|=2.17 (check standard normal table)

So 97% CI is
xbar±Z*s/n

--> 998±2.17*10/8

--> (995.2875, 1000.712)

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(b) 1. narrower

2. wider

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