Question

select all that apply. if the sample standard deviation of a sample n = 1001 is 2.60 and sample mean is 2.94, then the upper bound with 95% confidence level is 3.10. the lower bound with 95% confidence level is 2.78. the z value corresponding to a 95% confidence level is 2.58. estimate standard error is.8.

Explanation:

Step1: Calculate standard error

Standard error \(SE=\frac{s}{\sqrt{N}}\), where \(s = 2.60\), \(N=1001\).
\(SE=\frac{2.60}{\sqrt{1001}}\approx\frac{2.60}{31.64}\approx0.082\)

Step2: Find Z - value for 95% confidence level

For a 95% confidence level, the \(Z\) - value is \(Z = 1.96\) (not \(2.58\) which is for 99% confidence level)

Step3: Calculate confidence interval bounds

The confidence interval formula is \(\bar{x}\pm Z\times SE\), where \(\bar{x}=2.94\), \(Z = 1.96\), \(SE\approx0.082\)
Upper bound: \(\bar{x}+Z\times SE=2.94 + 1.96\times0.082=2.94+0.161=3.10\)
Lower bound: \(\bar{x}-Z\times SE=2.94-1.96\times0.082=2.94 - 0.161=2.78\)

Answer:

the upper bound with 95% confidence level is 3.10, the lower bound with 95% confidence level is 2.78