A production supervisor at a major chemical company wishes to determine whether

Question

A production supervisor at a major chemical company wishes to determine whether a new catalyst, catalyst XA-100, increases the mean hourly yield of a chemical process beyond the current mean hourly yield, which is known to be roughly equal to, but no more than, 750 pounds per hour. To test the new catalyst, five trial runs using catalyst XA-100 are made. Assuming that all factors affecting yields of the process have been held as constant as possible during the test runs, it is reasonable to regard the five yields obtained using the new catalyst as a random sample from the population of all possible yields that would be obtained by using the new catalyst. Furthermore, we will assume that this population is approximately normally distributed. Regard the sample of 5 trial runs for which s = 19.62 as a preliminary sample. Determine the number of trial runs of the chemical process needed to make us: (Round up your answers to the next whole number.) (a) 95 percent confident that 1formula102.mml, the sample mean hourly yield, is within a margin of error of 8 pounds of the population mean hourly yield µ when catalyst XA-100 is used. n trial runs (b) 99 percent confident that 1formula102.mml is within a margin of error of 5 pounds of µ. n trial runs

Explanation / Answer

Use the confidence interval for one sample t, not one sample z. It only said that it is approximately normally distributed which is basically for assumption of t. It also did not say anything about normally distributed with standard deviation(sigma) equal to anything. So assume that we don't know true standard deviation and s is only sample standard deviation.

df = n - 1 = 5 - 4 = 4

Find t* on t table for 4 degrees of freedom and for:

95% confidence: 2.776

99% confidence: 4.604

margin of error is the right side to the +/- part of the confidence interval formula.

The formula is xbar +/- t*(s/sqrt(n))

a)

For the first part it gives us m = 8

So set up an equation to solve for n:

8 = 2.776 * 19.62/sqrt(n)

sqrt(n) = 6.80814

n = 46.355 ---> 47

b)

Now it gives us m = 5

5 = 4.604 * 19.62/sqrt(n)

sqrt(n) = 18.0661

n = 326.3839  --> 327

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