The speed of wind in the desert determines wether dunes (large sand formations)
ID: 3256589 • Letter: T
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.