SOLUTION The proportion of Y responses in this sample is 24 = 0.75 32 Using the population proportion of 0.6 (given earlier), the standard deviation for the distri- bution of sample proportions is p(1-p) 0.6 (1 0.6) 0.09 %3D 32 The sample statistic, p = 0.75, therefore has a standard score of %3D sample proportion – population proportion 0.75 0.6 = 1.67 = 2 standard deviation 0.09
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.
![mean? What is the probability of selecting another sample with a proportion greater than the
one you selected?
SOLUTION The proportion of Y responses in this sample is
24
0.75
%3D
32
Using the population proportion of 0.6 (given earlier), the standard deviation for the distri-
bution of sample proportions is
P(1 p)
0.6 (1 0.6)
= 0.09
|3D
32
The sample statistic, p = 0.75, therefore has a standard score of
sample proportion – population proportion
0.75 0.6
= 1.67
= 2
standard deviation
0.09
The sample proportion is 1.67 standard deviations above the mean of the distribution. Using
Table A-1, we find that a standard score of 1.67 corresponds to the 95.25th percentile. The
probability of selecting another sample with a proportion less than the one we selected is about
0.9525, and the probability of selecting another sample with a proportion greater than the one
we selected is about 0.0475. In other words, if we were to select 100 random samples of 32
responses, we should expect to see only about 5 samples with a higher proportion than for the
sample we selected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ac0719c-6f67-47af-a708-e767c12d2124%2Fe8e71cfc-a1a1-44b3-9d5d-d7394f956e77%2Fhp8x6zw_processed.jpeg&w=3840&q=75)
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