Question

At wind speed above 1000 cm/sec, significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cycling nature of wind and moving sand determines the shape and location of large sand dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty wind speed readings gave an average velocity of 1075cm/sec. Based on long-term experience, σ can be assumed to be 265 cm/sec.

a) Calculate and interpret a 95% confidence interval for the true population mean wind speed at this site.

b) Obtain the interval using Excel and show your output.

c) Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain.

d) In order to trust the information in the interval, is there anything else about these data that we need to know?

e) What is the margin of error for this interval? Show calculation.

f) If we want to reduce the margin of error to 40 cm/sec, how big must the sample size be?

Answer 1

(a) n = 60, x-bar = 1075, s = 265, % = 95     

Standard Error, SE = σ/Ön =    265 /√60 = 34.21135289

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 34.2113528914988 = 67.05301953

Lower Limit of the confidence interval = x-bar - width =      1075 - 67.053019529728 = 1007.94698

Upper Limit of the confidence interval = x-bar + width =      1075 + 67.053019529728 = 1142.05302

The 95% confidence interval is [1007.95, 1142.05]

(c) Yes, the entire confidence interval is above 1000. So, the wind speed is such that the sand is always moving at this site.

e) margine of error:

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 34.2113528914988 = 67.05301953