30. When surveys are taken, there are usually several types of questions asked;

Question

30. When surveys are taken, there are usually several types of questions asked; and several interval estimates desired. Suppose a ski resort collects some data from skiers on overall satisfaction level and distance traveled. For one particular week, a random sample of 100 skiers at a Colorado resort revealed that 70 were satisfied or very satisfied with their stay at the resort. The average distance traveled by the same 100 skiers was 600 miles with a standard deviation of 250 miles. Find 95% interval estimates for the true proportion that are at least satisfied and for the average distance traveled. Interpret your answers. Are there any potential problems with these two estimates? Comment.

Explanation / Answer

for satisfied:

n =100 , p = 70/100 = 0.7

z value at 95% = 1.96

CI = p+/- z* sqrt(p * (1 - p) / n)
= 0.7 +/- 1.96 * sqrt( 0.7 * 0.3/100)
= (0.6102 , 0.7898)
Lower Bound = 0.6102
Upper Bound = 0.7898

The 95% interval estimates that are satisfied between 0.6102 and 0.7898

For average distance travelled

n = 100 , mean = 600 , s = 250

Ci = mean +/- z * ( s/sqrt(n))
= 600 +/- 1.96 * (250/sqrt(100))
= (551,649)

Lower Bound = 551
Upper Bound =649
The 95% interval estimates that the average distance travelled is between 551 and 649.

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