At winds speeds above 1000 centimeters per second (cm/sec), significant sand-mov
ID: 3369733 • Letter: A
Question
At winds speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to oceur. Wind spceis below 1000 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large 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 of 1075 cm/sec and based long term expcrience the standard deviation for wind speed is 265 cm/scc. a 95% confidence interval for the population mean wind speed at this site. a) Find (b) Doss the confidence interval indicate that the population mean wind spoed is such that the sand is always moving at this site? Explain. (c) Find a 99% confidence interval for the population mean wind speed at this site. (d) Compare the margins of error in parts (a) and (c). As the confidence levels increase, do the margins of error increase? If so, why would this occur?Explanation / Answer
(a) E = Z*sigma/sqrt(n) for 95% , Z=1.96
=1.96*265/(sqrt(60)) = 1.96*34.211 = 67.05
95% CI: (1075-67.05 < u < 1075+67.05)
= (1007.95 < u < 1142.05)
(b) According to Confidence interval, we are 95% confident that the population average of wind speeds is between 1007.95 and 1152.05. Since this entire interval is above 1000 we can be 95% confident that the sand is moving.But this on the average. There may be many times when the wind speed is below 1000.
(c)
E = Z*sigma/sqrt(n) for 95% , Z=2.58
=2.58*265/(sqrt(60)) = 2.58*34.211 = 88.26
95% CI: (1075-88.26 < u < 1075+88.26)
= (986.74 < u < 1163.26)
(d) Example- If you want to be surer of hitting a target with a spotlight, then you make your spotlight bigger.
Three things influence the margin of error in a confidence interval estimate of a population mean: sample size, variability in the population, and confidence level.
Apparently a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our accuracy is higher.
Also a 95% confidence interval is narrower than a 99% confidence interval which is wider. The 99% confidence interval is more accurate than the 95%.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.