A 90 % confidence interval for the average salary of all CEOs in the electronics

Question

A 90 % confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. the interval was ($133, 306, $150, 733). To make useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) Increase the sample size and increase the confidence level. B) Decrease the sample size and increase the confidence level. C) Decrease the sample size and decrease the confidence level. D) Increase the sample size and decrease the confidence level.

Explanation / Answer

The confidence interval for population mean is:

{Xbar ± (/n)(Z/2)}if population standard deviation is known and

{Xbar ± (s/n)(t/2)} if population standard deviation is unknown and it is replaced by its estimate, s, the sample standard deviation.

As can be seen from both formulae above, the width of the CI is solely determined by (/n)(Z/2) or (s/n)(Z/2) which in turn in inversely proportional to the value of n since n is in the denominator. So, increasing sample size will reduce the CI width.

Further, as we increase confidence level 100(1 - ), reduces and consequently percentage points Z/2 and t/2 increase, in turn increasing the CI width.

Thus, to reduce CI width, sample size should be increased and confidence level should be reduced. Option (D) ANSWER

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