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Question 3 Confidence Intervals Response

Content type
User Generated
Subject
Statistics
School
Cuyamaca College
Type
Homework
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Question 3 - Confidence Intervals
a) Sample information
Number of students who do not work, x = 32
Sample size, n = 50
b) 95% confidence interval estimate of the number of students who do not work
This is a confidence interval for a single proportion given by the formula
 
  
z critical value for 95% confidence level,
Area to the right of the right critical value
=(1-0.95)/2 =0.05/2
=0.025
Area to the left of the right critical value
=1-0.025
=0.975
Inverse z score with area to the left tail being 0.975


Sample proportion



Substitute values into the equation
 

  



 
Lower limit  
Upper limit  
95% confidence interval
(0.507, 0.773)
c) Interpretation
We are 95% confidence that the true population proportion of the number of
students who do not work is between 0.507 and 0.773.
d) Margin of error

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Question 3 - Confidence Intervals a) Sample information Number of students who do not work, x = 32 Sample size, n = 50 b) 95% confidence interval estimate of the number of students who do not work This is a confidence interval for a single proportion given by the formula = 𝑝̂ ± 𝑧𝛼 ∗ √ 2 𝑝̂ (1 − 𝑝̂ ) 𝑛 z critical value for 95% confidence level, 𝑧𝛼 2 Area to the right of the right critical value =(1-0.95)/2 =0.05/2 =0.025 Area to the left of the right critical value =1-0.025 =0.975 Inverse z score with area to the left tail being 0.975 𝑧𝛼 = 𝑧0.05 = 1 ...
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