Answer:
a) Margin of Error at 95% confidence level = 0.053
b) The 95% confidence interval for the average number of close confidants = (2.147, 2.253)
The 95% confidence interval is from 2.147 to 2.253.
Explanation:
The full correct question is attached to the solution of this question.
Sample Mean = 2.2
Standard deviation = 1.4
Sample size = 2006
a) Find the margin of error for this estimate if we want 95% confidence
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value at 95% confidence interval for sample size of 2006 is obtained from the z-tables.
Critical value = 1.960
standard Error is calculated this
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 1.4
n = sample size = 2006
σₓ = (1.2/√2006) = 0.0268
Margin of Error = (Critical value) × (standard Error of the mean)
= 1.960 × 0.0268 = 0.0525 = 0.053 to 3 d.p.
b) Compute the 95% confidence interval for the average number of close confidants
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 2.2
Margin of Error = 0.053
Confidence Interval = 2.2 ± 0.053
95% Confidence interval = (2.147, 2.253)
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