Question

Use the sample information x¯ = 35, σ = 7, n = 16 to calculate the following confidence intervals for μ 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 4 decimal 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.

Answer 1

a)

z value at 90% = 1.645

CI = mean +/- z *(s/sqrt(n))
= 35 +/- 1.645 *(7/sqrt(16))
= (32.1215 , 37.8785 )

The 90% confidence interval is from 32.1215 to 37.8785

b)

z value at 95% = 1.96

CI = mean +/- z *(s/sqrt(n))
= 35 +/- 1.96 *(7/sqrt(16))
= (31.5701 , 38.4299 )

The 95% confidence interval is from 31.5701 to 38.4299

c)
z value at 99% = 2.576

CI = mean +/- z *(s/sqrt(n))
= 35 +/- 2.576 *(7/sqrt(16))
= (30.4923 , 39.5077 )

The 95% confidence interval is from 30.4923 to 39.5077 )

d)
The interval gets wider as the confidence level increases.