Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confident that Tweed residents are more concerned about the environment than the residents of Ledee. He knows that the average electricity consumption of Tweed households last February was 654.32 kWh and decides to test if Ledee residents used more electricity that month, on average. He collects data from 45 Ledee households and calculates the average electricity consumption to be 687.81 kWh with a standard deviation of 117.17 kWh. There are no outliers in his sample data. Neal does not know the population standard deviation nor the population distribution. He uses a one-sample t-test with a significance level of a = 0.05 to test the null hypothesis, Ho: µ = 654.32, against the alternative hypothesis, H1:µ > 654.32, where µ is the average electricity consumption of Ledee households last February. Neal calculates a t-statistic of 1.917 and a P-value of 0.031. Based on these results, complete the following sentences to state the decision and conclusion of the test. Neal's decision is to the (P=0.031). There is evidence to the hypothesis that the average electricity consumption of iS *....... 1.......
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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