2. Because couples are deciding to have fewer children, the family size of the United States has declined continuously during the past few decades. According to the U.S. Bureau of the Census, the mean family size was 3.19 with a standard deviation of 0.70 in 1995. A researcher wanted to check if the current mean family size is less than 3.19. A sample of 900 families taken this year by this researcher produced a mean family size of 3.16. Using the .025 significance level, can we conclude that the mean family size has declined since 1995?
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.
2. Because couples are deciding to have fewer children, the family size of the United States has declined continuously during the past few decades. According to the U.S. Bureau of the Census, the mean family size was 3.19 with a standard deviation of 0.70 in 1995. A researcher wanted to check if the current mean family size is less than 3.19. A sample of 900 families taken this year by this researcher produced a mean family size of 3.16. Using the .025 significance level, can we conclude that the mean family size has declined since 1995?
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