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Complete Question
How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?
Exercise 9.53
A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.
B. What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?
Answer:
The First question
A
The 96% confidence interval is
B
The possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is
Step-by-step explanation:
From the question we are told that
The margin of error is
The sample size is n = 200
The number that supported the annexation suit is k = 114
Considering the first question
Generally our sample in Exercise 9.53 is
From the question we are told the confidence level is 96% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the sample size is mathematically represented as
=>
=>
=>
Considering question B
Generally the margin of error is mathematically represented as
=>
=>
Considering question A
Generally the sample proportion of the number that supported the annexation suit is mathematically represented as
=>
Generally 96% confidence interval is mathematically represented as
=>
=>