Question

How Many Close Confidants Do People Have? In a recent study,1 2006 randomly selected US adults (age 18 or older) were asked to give the number of people in the last six months ‘‘with whom you discussed matters that are important to you." The average number of close confidants was 2.2, with a standard deviation of 1.4.

Answer 1

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)

Hope this Helps!!!