Question

If you are given summary statistics for a sample and want to construct a confidence interval, this can be done through the Probability Calculator in Geogebra. Open it and click the “Statistics” tab just above the graph. For a confidence interval for a population mean, with unknown σ, click the drop-down menu near the top (default is “Z Test of a Mean”) and choose “T Estimate of a Mean.” Enter the confidence level (in decimal form), sample mean, sample standard deviation, and sample size. We’ll use a sample with x¯=65.17, s=3.654, n=26. Based on this sample data, a 95% confidence interval for the population mean is: equation editorEquation Editor <μ< equation editorEquation Editor . The margin of error for this 95% confidence interval is equation editorEquation Editor . Based on this sample data, a 99% confidence interval for the population mean is: equation editorEquation Editor <μ< equation editorEquation Editor . The margin of error for this 99% confidence interval is

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 65.17

sample standard deviation = s = 3.654

sample size = n = 26

Degrees of freedom = df = n - 1 = 26-1 = 25

1) At 95% confidence level the t is,

= 1 - 0.95 = 0.05

/ 2 = 0.025

t _/2,df = t 0.025,25 = 2.060

Margin of error = E = t_/2,df * (s /n)

= 2.060 * ( 3.654 /  26)

Margin of error = E = 1.48

The 95% confidence interval estimate of the population mean is,

- E < < + E

65.17 - 1.48 < < 65.17 + 1.48

63.69 < < 66.65.

2) At 99% confidence level the t is,

= 1 - 0.99 = 0.01

/2 = 0.005

t _/2,df = t 0.005,25 = 2.787

Margin of error = E = t_/2,df * (s /n)

= 2.787 * ( 3.654 / 26)

Margin of error = E = 2.00

The 99% confidence interval estimate of the population mean is,

- E < < + E

65.17 - 2.00 < < 65.17 + 2.00

63.17 < < 67.17.