The speed of wind in the desert determines wether dunes (large sand formations)

Question

The speed of wind in the desert determines wether dunes (large sand formations) occur. When the wind speed is stronger than 10 m/sec dunes move to new locations. A random sample of 50 wind speed readings at a certain site have a mean of 10.75 m/sec and a standard deviation of 2.65 m/sec. a. Find the margin of error for a confidence level of 95%. b. Find the 95% confidence interval for the population mean wind speed at this site. c. Use information from part (a) to fill in the blanks in the following sentence: ___% of all samples of size ___ have sample means within ___ of the population mean d. Does the confidence interval, at 95% confidence level, provide sufficient evidence that the mean wind speed at this site is sufficient to produce dunes to move? Write an appropriate inequality to justify your answer.

Explanation / Answer

a) here std error =std deviation/(n)1/2 =2.65/(50)1/2 =0.3748

for 95% CI and (n-1=49) degree of freedom ; t=2.0096

hence margin of error =t*std error =0.7531

b)95% Confidence interval =sample mean -/+ t*std error =10.75 -/+ 0.7531 =9.9969 ; 11.5031

c)

95% of all sample of size 50 have sample means within 0.7531 of the population mean

d)

as our interval contains 10 m/sec as probable value of population mean we can not accept that mean is greater then 10 and hence does not provide sufficient evidence.

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