Q38E A random sample of n = 80 measur... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 5: Q38E (page 320)

A random sample of n = 80 measurements is drawn from a binomial population with a probability of success .3.
Give the mean and standard deviation of the sampling distribution of the sample proportion, $\overset{炉}{p}$
Describe the shape of the sampling distribution of $\overset{炉}{p}$
Calculate the standard normal z-score corresponding to a value of $\overset{炉}{p}$ =0.35
Find $P (\overset{炉}{p)}$ =0.35

Short Answer

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A random sample is a subgroup of people chosen at random by investigators to represent the full population as a whole. A technique for selecting a sample of data from a community to make predictions regarding the community.

Step by step solution

Step 1: (a) The data is given below

The calculation is given below:

Given,

n=80

p=0.3

$\begin{array}{rcl} Mean (p) = 0.3 \\ 蟽 \overset{铃�}{P} & = & \frac{\sqrt{pq}}{n} \\ = & \frac{\sqrt{0.3 脳 (1 - 0.3)}}{80} \\ = & 0.0512 \end{array}$

$鈮� 0.05$

(b) The data is given below

The calculation is given below:

$np = 80脳0.3 = 24 猢� 10 nq = 80脳0.7 = 56 猢� 10$

Since $np 猢� 10 and nq 猢� 10,$ the sample probability is normal distribution is normally distributed with $渭 \overset{铃�}{P} = 0.3 and 蟽 \overset{铃�}{P} = 0.05$

(c) The data is given below

The calculation is given below:

For $\overset{铃�}{P} = 0.35, the Z score is:$

$\begin{array}{rcl} Z & = & \frac{\overset{铃�}{P} - 渭 \overset{铃�}{P}}{蟽 \overset{铃�}{P}} \\ = & \frac{0.35 - 0.3}{0.05} \\ = & 1 \end{array}$

(d) The data is given below

The calculation is given below:

$P (\overset{铃�}{P} > . 35) = P (\frac{\overset{铃�}{P} - 渭 \overset{铃�}{P}}{蟽 \overset{铃�}{P}} 猢� \frac{0.35 - 渭 \overset{铃�}{p}}{蟽 \overset{铃�}{p}}) = P (Z 猢� 1) = 1 - P (Z < 1)$

$= 1 - 0.8413 = 0.1587$

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91影视

Short Answer

Step by step solution

Step 1: (a) The data is given below

(b) The data is given below

(c) The data is given below

(d) The data is given below

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