Question

#2). Under-coverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample. We can check for under-coverage by comparing the sample with known facts about the population.

a. Suppose we take a SRS of n=500 people from a population that is 25% Hispanic. How many Hispanics are expected in a given sample? [2 points]

b. What is the standard deviation for the number of Hispanics in a sample? [2 points]

c. Can the normal approximation to the binomial be used to help make probabilistic statements about samples from this population? [2 points]

d. Determine the probability that a sample contains 100 or fewer Hispanics under the stated conditions.[4 points]

Answer 1

a)

expected = np =    500   *   0.250   =           125

b)

Standard deviation = √(np(1-p)) =   √   93.7500   =               9.6825

c)

Yes it can made because np>=10

d)

Sample size , n =    500                      
Probability of an event of interest, p =   0.25                      
left tailed                          
X <   101                      
                          
Mean = np =    125                      
std dev ,σ=√np(1-p)=   9.6825                      
                          
P(X <   101   ) = P(Xnormal <   100.5   )          
                          
Z=(Xnormal - µ ) / σ = (   100.5   -   125   ) /   9.6825   =   -2.5303
                          
=P(Z<   -2.5303   ) = 0.0057          

  

Thanks in advance!

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