26. Let u = 78. A sample of 26 provided a sample mean x = 77.8 and a sample standard deviation s = 2. Find P (x < 77.8). %3D a. 0.1 < P (x < 77.8) < 0.15 b. 0.15 < P (x < 77.8) < 0.2 c. 0.2 < P (ï < 77.8) < 0.25 d. 0.25 < P (x < 77.8)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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26. Let u = 78. A sample of 26 provided a sample mean i = 77.8 and a sample standard deviations = 2.
Find P (x < 77.8).
%3D
a. 0.1 < P (x < 77.8) < 0.15
b. 0.15 < P (x < 77.8) < 0.2
c. 0.2 < P (x < 77.8) < 0.25
d. 0.25 < P (x < 77.8)
6 -
27. Interpretation of left-tail probability (based on the t test statistic)
Refer to the left-tail probability P (x < 77.8) question above.
Let's assume that as researchers, we consider a probability smaller than 5% small. Since
P (x < 77.8) is
close to the assumption of u = 78. In other words, given that the population mean is 78, it is
highly likely that a sample mean this close to the population mean would occur by pure chance
than 5%, it is
to have obtained such a sample mean that
alone.
To put it another way, the occurrence of this sample mean of 77.8
cast(s) doubt on the
validity of the assumption of 77.8.
a.
smaller, surprising, does
b. larger, not surprising, does not
c. larger, surprising, does
d. smaller, not surprising, does not
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