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Chapter 8: Q. T8.8 (page 549)

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of at most \(2. Based on last year鈥檚 book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to which of the following?

a. 25

b.30

c. 225

d. 609

e. 865

Short Answer

Expert verified

The required number of observations is 25

The correct option is(a)

Step by step solution

01

Given information

Standard deviation (蟽)=30

Confidence level =90%

Margin of error(E)=2

02

The objective is to find out the number of observations.

We know,

The formula to compute the sample size is:

n=z伪2脳蟽E2

The standard normal table yields the value of za2corresponding to a 90%confidence level of1.645.

The total number of observations can be calculated as follows:

n=z伪2脳蟽E2=1.645脳3022=24.675鈮�25

The sample size is 25

Therefore, the correct option is(a)

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