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Statistics

1. Suppose you have drawn a simple random sample of 10 students from a college campus and recorded how many hours each student surfed the internet during the first week of February, 2010.

Results:
Student: 1 2 3 4 5 6 7 8 9 10
Hours of Internet Surfing: 9 12 4 10 5 18 8 12 6 6

For this sample, compute (Xi), the sample average (X-bar), (Xi - X-bar)2, and the sample standard deviation (s).

2. Suppose the annual snowfall in a city is normally distributed with a mean of 80 inches and a standard deviation of 25 inches. Find the probability that in a given year, snowfall in the city would be between 60 and 100 inches (that is, within ± 20 of m = 80).

3. Let X denote the amount of money an SU student spends on books in a year. Assume that population mean is $800, and the population standard deviation is $125. Suppose you have drawn a simple random sample of size 400 from the SU student
population. Compute the probability that the sample mean (X) is between $790 and $810.

4. Suppose 20% of SU students own Apple computers, that is, p = 0.2. You have drawn a simple random sample of size 400 from this population. Let p denote the proportion of the sample that own Apple computers. Compute the probability that for your sample of 400 students, p will fall between 0.18 to 0.22 (i.e., within ±.02 of p = .2)

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4. Suppose you have drawn a simple random sample of 10 students from a college campus and recorded how many hours each student surfed the internet during the first week
of February, 2010.

Results:

Student 1 2 3 4 5 6 7 8 9 10
Hours of Internet Surfing 9 12 4 10 5 18 8 12 6 6

For this sample, compute ∑ Xi, the sample average (X-bar), ∑ (Xi - X-bar)2, and the sample standard deviation (s).

Solution:

∑ Xi = (9+12+4+10+......+6+6) = 90

(X-bar) = ∑ Xi /n = 90/10 = 9

x_i x ̅ ( x_i-x ̅ ) ( x_i-x ̅ )2
9 9 (9-9) = 0 (0)2 = 0
12 9 (12-9) = 3 (3)2 = 9
4 9 (4-9) = -5 (-5)2 = 25
10 9 (10-9) = 1 (1)2 = 1
5 9 (5-9)= -4 (-4)2 = 16
18 9 (18-9)= 9 (9)2 ...

Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

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