Use the sample information x = 36, sigma = 6, n = 11 to calculate the following

Question

Use the sample information x = 36, sigma = 6, n = 11 to calculate the following confidence intervals for mu assuming the sample is from a normal population. (a) 90 percent confidence. (Round your answers to 4 decimal places.) The 90% confidence interval is from to (b) 95 percent confidence. (Round your answers to 4decimal places) The 95% confidence interval is from to (c) 99 percent confidence. (Round your answers to 4 decimal places.) The 99% confidence interval is from to (d) Describe how the intervals change as you increase the confidence level. The interval gets narrower as the confidence level increases. The interval gets wider as the confidence level decreases. The interval gets wider as the confidence level increases. The interval stays the same as the confidence level increases.

Explanation / Answer

Solution:

Given Sample Mean x = 36
SD = 6
Sample Size (n) = 11
a) Confidence interval = 1-0.9 = 0.1
z critical value for 90% confidence interval:
z(/2) = z(0.05) = 1.6449
Confidence interval = ± Z/2 */sqrt(n)
= 36 ±1.6449 * 6/sqrt(11)
= (33.02 , 38.98)

b) Confidence interval = 1-0.95 = 0.05
z critical value for 95% confidence interval:
z(/2) = z(0.025) = 1.96
Confidence interval = ± Z/2 */sqrt(n)
= 36 ±1.96 * 6/sqrt(11)
= (32.45 ,39.55)
c) Confidence interval = 1-0.99 = 0.01
z critical value for 99% confidence interval:
z(/2) = z(0.005) = 2.576
Confidence interval = ± Z/2 */sqrt(n)
= 36 ±2.576 * 6/sqrt(11)
= (31.33 ,40.66)
d) c. The interval gets wider as the confidence level increases.

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