13. A sample of the reading scores of 35 fifth-graders has a mean of 82. The standard deviation of the sample is 15. a) Find the 95% confidence interval of the mean reading scores of all fifth-graders. b) Find the 99% confidence interval of the mean reading scores of all fifth-graders. c) Which interval is larger? Explain why.
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.
13. A sample of the reading scores of 35 fifth-graders has a mean of 82. The standard deviation of the sample is 15.
a) Find the 95% confidence interval of the mean reading scores of all fifth-graders.
b) Find the 99% confidence interval of the mean reading scores of all fifth-graders.
c) Which interval is larger? Explain why.
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