Question 148777This question is from textbook Understanding Basic Statistics
: Does anyone out there is statistics land have a clue how to figure this problem out??? I would appreciate any help. Thank you in advance!
At wind speeds 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 cyclic nature of wind and moving sand determines teh 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 velocity of x(bar)=1075 cm/sec. Based on long term experience, sigma (standard deviation)can be assumed to be 265 cm/sec.
Find a 95% confidence interval for the population mean wind speed at this site AND does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site. Explain.
This question is from textbook Understanding Basic Statistics
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sixty wind speed readings gave an average velocity of x(bar)=1075 cm/sec. Based on long term experience, sigma (standard deviation)can be assumed to be 265 cm/sec.
Find a 95% confidence interval for the population mean wind speed at this site AND does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site. Explain.
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E = 1.96*265/(sqrt(60)) = 1.96*34.211 = 67.05
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95% CI: (1075-67.05 < u < 1075+67.05)
= (1007.95 < u < 1142.05)
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The CI says 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.
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Cheers,
Stan H.
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