Please show how to solve step-by-step. CHAPTER 7 Sampling and Sampling Distribut

Question

Please show how to solve step-by-step. CHAPTER 7 Sampling and Sampling Distributions Sampling Distribution of CONTENTS the EAI Problem STATISTICS IN PRACTICE: Practical value of the Samp MEADWESTVACO CORPORATION Distribution of 7.1 THE ELECTRONICS Relationship Between the Sample ASSOCIATES SAMPLING Size and the sampling PROBLEM Distribution of 7.2 SELECTING A SAMPLE 7.6 SAMPLING DISTRIBUTION Sampling from a Fini OF p Expected Value of p Sampling from an Infinite Standard Deviation of p Form of the Sampling 7.3 POINT ESTIMATION Distribution of p Practical Advice Practical Value of the Sampling 7.4 INTRODUCTION TO Distribution of p SAMPLING DISTRIBUTIONS 7.7 OTHER SAMPLING 7.5 SAMPLING DISTRIBUTION METHODS OF i Stratified Random Sampling Expected Value of Cluster Sampling Standard Deviation of r ystematic sampling Form of the Sampling Convenience Sampling Distribution of Judgment Sampling TATIST MEADWE icant produc woodland ha terial, for m need reliabl berlands and meet its futu volume in th forests? Wh forests? Wi MeadWestva future, inclu How doe needs about it sample plots ation and numbers, Mea ples of 115- to plots estvac to learn a

Explanation / Answer

Solutions

a) Standard error of proportion = sqrt( p(1-p) / n) = 0.0625
square both sides
p(1-p) / n = (0.0625)^2
p(1-p)/ n = 0.003875
(0.25)(0.75) / n = .003875
multiply both sides by n
(0.25)(0.75) = 0.003875n
n = (0.25)(0.75) / .003875 = 48.39
n = 48

b)The mean will be 25% if historical trends hold. The 48 sample size is large enough to assume the distribution is normal, rather than use a "t" distribution or other model. Sampling distribution of p^ is normal with

mean p = 0.25

standard error sqrt( (0.25)(0.75) / 48.39) =0.0625

c) = 0.25

= 0.0625

standardize x to z = (x - ) /

P(x > 0.3) = P( z > (0.3-0.25) / 0.0625)

= P(z > 0.8) = 0.2119
(From Normal probability table)

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