Question

Given a sample size of n = 529. Let the variance of the population be σ2 = 10.89. Let the mean of the sample be xbar = 15. Construct a 95% confidence interval for µ, the mean of the population, using this data and the central limit theorem.

Use Summary 5b, Table 1, Column 1

1. What is the standard deviation (σ) of the population?
2. What is the standard deviation of the mean xbar when the sample size is n, i.e. what is σ_xbar , in terms of σ and n using the central limit theorem?
3. Is this a one-sided or two-sided problem?
4. What value of z should be used in computing k, the margin of error, where

z = k/σ_xbar ?

5. What is k?
6. Write the 95% confidence interval for µ based on xbar and k,

(xbar – k) < µ < (xbar + k)

7. Using the Z-score applet “Area from a value”. Let the Mean = 15, and SD = σ_xbar. Choose “Between (xbar -k) and (xbar + k)” using xbar = 15 and your computed value of k. Hit “Recalculate”. Does the probability approximately equal 0.95? (yes or no). Include a screen shot of your answer.

Answer 1