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Chapter 7: Q. T7.3 (page 486)

Suppose we select an SRS of size n=100n=100from a large population having proportion p of successes. Let p∧p^be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p∧p^?

a. 0.01

b. 0.09

c. 0.85

d. 0.975

e. 0.999

Short Answer

Expert verified

Option (c)0.85is the right answer.

Step by step solution

01

Given Information

Given,

The value of n is 100

02

Explanation for correct option

If both np and n(1-p) are more than 10, the sampling distribution of p^ is close to normal.

(a) np=100×0.01=1n(1-p)=100×(1-0.01)=99

(b) np=100×111=9.0909n(1-p)=100×1-111=90.9091

(c) np=100×0.85=85n(1-p)=100×(1-0.85)=15

(d) np=100×0.975=97.5n(1-p)=100×(1-0.975)=2.5

(e) np=100×0.999=99.9n(1-p)=100×(1-0.999)=0.1

Hence, the correct option is (c)

03

Explanation for incorrect option

Option (A) 0.01is the right answer

Option (B) 0.09is the right answer

Option (D) 0.975is the right answer

Option (E) 0.999is the right answer

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Most popular questions from this chapter

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

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