Answer the question. Show all the steps, not only the final answer. if possible, sketch a little diagram to clearly see the area under the normal curve.
1. A major research study concluded that the mean number of times that adolescents had engaged in vandalism during the previous 12 months was 3.5 times. We believe the true population mean to be less than this. After collecting our own sample of 36 adolescents, we find that the mean number of times they have vandalized property during a l-year period wasX̅ = 2.9 with a standard deviation equal to .7. Perform all ofthe procedures necessary for conducting a hypothesis test based on our assumption. What do you conclude? Set your alpha level at .05.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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