### Chapter 7, Survey Sampling

#### Solution 19

For the first part, we need to find the constant such that the interval is a 90% confidence interval for .

We shall use the same function here as used in the book. Also let denotes the standard normal function.

Thus we have:

Thus for 90% confidence interval we need . And . By the definition of , we have . Thus

Now we just need to lookup in the standard normal table to find .

Second part is also similar where we need to find the value of for the one sided confidence interval .

We can proceed from the last result:

Thus for 95% confidence interval we need . And . By the definition of , we have . Thus .

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