Q2. The US Energy Information Administration compile data on energy consumption and publishes its findings in Residential Energy Consumption Survey: Consumption and Expenditure. In 1982, the mean energy consumed per American household was 114 million BTU. For that same year, 50 randomly selectod houscholds in the South had the following energy consumption: 130 55 45 64 155 66 60 80 102 62 58 101 75 111 151 139 81 55 66 90 97 77 51 67 125 50 136 55 83 91 54 86 100 78 93 113 104 96 113 96 87 129 109 69 94 99 97 83 97 Do the data provide sufficient evidence to conclude that in 1982 the mean energy consumption by southern houscholds differed from that of all American houschold? Use the following steps to answer the questions:
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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