Math Problem Statement
Suppose a simple random sample of size
nequals=150150
is obtained from a population whose size is
Upper N equals 25 comma 000N=25,000
and whose population proportion with a specified characteristic is
p equals 0.6 .p=0.6.****
Complete parts (a)**** through (c)****
below**.**
Question content area bottom
Part 1
(a) Describe the sampling distribution of
ModifyingAbove p with caretp.
Choose the phrase that best describes the shape of the sampling distribution below.
A.
Approximately normal because
n less than or equals 0.05 Upper Nn≤0.05N
and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10.
Your answer is correct.
B.
Not normal because
n less than or equals 0.05 Upper Nn≤0.05N
and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10.
C.
Not normal because
n less than or equals 0.05 Upper Nn≤0.05N
and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10.
D.
Approximately normal because
n less than or equals 0.05 Upper Nn≤0.05N
and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10.
Part 2
Determine the mean of the sampling distribution of
ModifyingAbove p with caretp.
mu Subscript ModifyingAbove p with caret Baseline equalsμp=0.60.6
(Round to one decimal place as needed.)
Part 3
Determine the standard deviation of the sampling distribution of
ModifyingAbove p with caretp.
sigma Subscript ModifyingAbove p with caretσpequals=enter your response here
(Round to six decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Sampling Distributions
Proportions
Formulas
Sampling distribution mean: μ̂p = p
Standard deviation of sampling distribution: σ̂p = sqrt[p(1 - p) / n] * sqrt[(N - n) / (N - 1)]
Theorems
Central Limit Theorem
Finite Population Correction Factor
Suitable Grade Level
Undergraduate Statistics
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