A college administrator would like to estimate the average grade point average (average of GPA) of all the current registered st
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Answer
Answer
The speedometer is likely to show the speed is either 36.0 mph or 44.0 mph.
To prove
Formula
Where error = |Approx value - Exact value |
First case
As given
A speedometer has a percent error of 10%. The actual speed of the car is 40 mph.
Here
Percentage error = 10%
Exact value = 40 mph
error = - (Approx value - Exact value )
= - (Approx value - 40 )
= - Approx value + 40
Put in the formula
Thus
Approx value = 40 - 4
Approx value = 36 mph
Therefore Option (b) is correct .
Second Case
error = (Approx value - Exact value )
= (Approx value - 40 )
= Approx value - 40
Put in the formula
Thus
Approx value = 40 + 4
Approx value = 44 mph
Therefore Option (c) is correct .
Answer:
The corresponding point estimate is 0.882.
The sample standard deviation is 1.373.
Step-by-step explanation:
The data set is:
S = {25.01, 25.87, 26.34, 26.51, 26.75, 27.24, 27.40, 27.63, 27.83, 27.90, 28.08, 28.13, 28.37, 28.58, 28.59, 28.96, 29.20, 29.22, 29.38, 30.88}
Compute the mean as follows:
Subtract the mean from each value and take the modulus of those values.
The new data set is:
S₁ = {2.8835, 2.0235, 1.5535, 1.3835, 1.1435, 0.6535, 0.4935, 0.2635, 0.0635, 0.0065, 0.1865, 0.2365, 0.4765, 0.6865, 0.6965, 1.0665, 1.3065, 1.3265, 1.4865, 2.9865}
Arrange these values in ascending order as follows:
S₂ = {0.0065 , 0.0635 , 0.1865 , 0.2365 , 0.2635 , 0.4765 , 0.4935 , 0.6535 , 0.6865 , 0.6965 , 1.0665 , 1.1435 , 1.3065 , 1.3265 , 1.3835 , 1.4865 , 1.5535 , 2.0235 , 2.8835 , 2.9865}
There are 20 observations in the data set.
The median value for an even set of values is the mean of the middle two values.
In this case the median will be the mean of the 10th and 11th observations.
Thus, the corresponding point estimate is 0.882.
Compute the standard deviation as follows:
In set S₁ we computed the absolute mean deviations.
Now take the square of these values and divide by (n - 1) to compute the sample variance:
Compute the sample standard deviation as follows:
Thus, the sample standard deviation is 1.373.