3. A random sample of nine telephone calls in an office provided the following i
ID: 3225946 • Letter: 3
Question
3. A random sample of nine telephone calls in an office provided the following information. Call Number Duration (In Minutes) Type of Call 1 3 local 2 8 long distance 3 4 local 4 3 local 5 5 long distance 6 6 local 7 3 local 8 5 local 9 8 local a. Determine the point estimate for the average duration of all calls. b. What is the point estimate for the standard deviation of the population? c. Determine the standard error of the mean. d. What is the point estimate for the proportion of all calls that were long distance? e. Determine the standard error of proportion.
Explanation / Answer
a) point estimate = ( 3 = 8 + 4 + 3 + 5 + 6 + 3 + 5 + 8) / 9 = 5
b) Variance = sum ( x -mean)^2 / n
= 3.56
std. deviation = sqrt(variance) = sqrt(3.56) = 1.88
c) SE = std. deviation / sqrt(n)
= 1.88 / sqrt(9) = 0.628
d) Point estimate = 2/9 = 0.222
e) p = 0.222 , 1 -p = 0.777 , n =9
SE = sqrt ( (0.222 * 0.777) / 9 )
= 0.138
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