A random sample of size n = 225 yielded = .46.a. Is the

Chapter 6, Problem 43E

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QUESTION:

Problem 43E

A random sample of size n = 225 yielded  = .46.

a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.

b. Construct a 95% confidence interval for p.

c. Interpret the 95% confidence interval.

d. Explain what is meant by the phrase “95% confidence interval.”

Questions & Answers

QUESTION:

Problem 43E

A random sample of size n = 225 yielded  = .46.

a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.

b. Construct a 95% confidence interval for p.

c. Interpret the 95% confidence interval.

d. Explain what is meant by the phrase “95% confidence interval.”

ANSWER:

Solution

Step 1 of 4

a) we have to tell that the sample size is large enough for finding the confidence intervals for p

Given that  n=225 and

Here

             =1-0.46

            =0.54

Now

And

here both the values are more than 15

Hence the sample size is sufficiently large to conclude the normal approximation is reasonable


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