Respond to the discussion post below with YOUR educated opinion in 3 sentences WITH scholarly source backing it up
This was a very confusing topic for me but here goes. “Z-scores are a conversion of individual scores into a standard form. The conversion is based on your knowledge about the population’s standard deviation and mean. A z-score tells you how many standard deviations from the mean your result is. Like z-scores, t-scores are also a conversion of individual scores into a standard form. However, t-scores are used when the conversion is made without knowledge of the population standard deviation and mean. Seeing as you don’t know those parameters for your population, you make an estimate by using the statistics from your sample” (Statistics How To, 2015). What this seems to means to me is that the difference between the two intervals is when you should use them and how they are derived. Both of them are used to determine the probability of a hypothesis however which one is used is determined by numerous factors and what data is presented. For example, is the sample greater than or less than 30? The answer to this question will help determine whether to use t or z. Also, whether or not the population standard deviation is known can help make the decision on which to use.
An example would be determining the weights of a random sample of high school males.
Assuming the weights of a random sample of 33 male high school students were recorded. Using the mean weight of 145 pounds and a standard deviation of 20 pounds. With a 95% confidence interval for the mean weight of all male students at this high school. The resulting interval would be 137.89 to 152.11.
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