3. Police Chief Aaron Ard of River City reports 500 traffic citations were issue
ID: 3152912 • Letter: 3
Question
3. Police Chief Aaron Ard of River City reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation of $4.50. Construct a 95 percent confidence interval for the mean amount of a citation in River City.
4. The Independent Department Store wants to determine the proportion of their charge accounts that have an unpaid balance of $1,500 or more. A sample of 250 accounts revealed that 100 of them had an unpaid balance of $1,500 or more. What is the 99 percent confidence interval for the population proportion? Would it be reasonable to conclude that more than half of the account balances are more that $1,500?
Please give me the answer with detailed explanation. I have no idea about this.
Explanation / Answer
3.
Note that
Margin of Error E = z(alpha/2) * sc / sqrt(n)
Lower Bound = X - z(alpha/2) * sc / sqrt(n)
Upper Bound = X + z(alpha/2) * sc / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 54
z(alpha/2) = critical z for the confidence interval = 1.959963985
n = sample size = 35
N = 500
sc = corrected sample standard deviation = s*sqrt[(N-n)/(N-1)] = 4.343989006
Thus,
Margin of Error E = 1.439139145
Lower bound = 52.56086086
Upper bound = 55.43913914
Thus, the confidence interval is
( 52.56086086 , 55.43913914 ) [ANSWER]
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