Can you solve this to make sure i understand the concept Aft

Can you solve this to make sure i understand the concept

After doing some financial analysis, the Chief Financial Officer has discovered the sampling of the steel runs in the above problem are too expensive {each sample costs $2,000]. She would like to reduce the sampling budget by $200,000. Assume the standard deviation does not change as the number of samples is reduced. Determine the impact of the sampling reduction on the 95% confidence interval. The Q/A manager is upset, and demands that the confidence interval must remain as wide as it was before regardless of the sample size reduction. Determine the reduction of the confidence level in that case. A new steel is being poured in the foundry and samples are extraordinarily expensive. However, it is required that the 99% confidence interval on the mean is at most +/- 100kg/m^3. It is assumed from researched processes that the standard deviation will be about 80kg/m^3. Determine the number of samples required to meet that condition without spending too much capital.

Solution

3)

To reduce the sampling expense by 200,000; at least 100 samples must be reduced.

A decrease in the sample size will increase the Standard error as:

S.E = Z * s / sqrt(n)

Thus, is n decreases, S.E will increase.

b)

To maintain the same Length of the interval, the level of confidence must decrease or, S.E must remain same as before.

Thus,

Z_i * s / sqrt(n) = Z_f * s / sqrt (n-100)

Value of Z_f has to be calculated. This is possible only if initial number of samples were known i.e \'n\' is known

Hope this helps.

4)

s = 80

Margin of error = 100

Confidence interval = 99%

Thus,

100 = 2.58 * 80 / sqrt(n)

n = (2.58 * 80 / 100)²

= 4.26

Thus, at least 5 samples are required.

Hope this helps