Question

At wind speeds above 1000 centimeters per second (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 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-two wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 240 cm/sec.

(a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)

lower limit _________    cm/sec

upper limit _________     cm/sec

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

• No. This interval indicates that the population mean wind speed is such that the sand may not always be moving at this site.
• Yes. This interval indicates that the population mean wind speed is such that the sand may not always be moving at this site.     
• Yes. This interval indicates that the population mean wind speed is such that the sand is always moving at this site.
• No. This interval indicates that the population mean wind speed is such that the sand is always moving at this site.

Answer 1

Solution

(a) The Z value for 95% CI is 1.96( taken out from Z tables)

The CI is given by :

Xbar +/- Z*Sigma/Sqrt(n)

= 1075 +/- 1.96*240/sqrt(62) = 1015 to 1135.

Upper bounds = 1135, Lower bound of CI is 1015

b) Since even the lower bound is above 1000( 1015 cm/sec > 1000cm/sec), the CI indicates that the population mean wind speed is such that the sand is always moving at this site.

Yes. This interval indicates that the population mean wind speed is such that the sand is always moving at this site.” (Option C_