At what smaller sample size does the difference between the population mean of 100 and the sample mean of 103 become not statistically significant?

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Free Supplementary Textbooks:
• Howell, D. C. (2012). Statistical Methods for Psychology. Cengage Learning. http://gtu.ge/Agro- Lib/Howle.pdf (well written and useful, heavy on formulas and hand calculation, little support for SPSS)
• Graphing Distributions in Lane’s Online Statistics Education: An Interactive Multimedia Course of Study at http://onlinestatbook.com/2/index.html or https://openstax.org/details/introductory- statistics
• Tyrrell, S. (2009). SPSS: Stats practically short and simple. Bookboon. Freely downloadable at https://oerstatistics.files.wordpress.com/2016/03/stats-practically-short-and-simple.pdf (This book is nice for a walk-through of the basic steps in data handling, data entry, and other “basic laboratory practices” or “basic office practices”. It is a good reference for a variety of details we might not cover directly in class and should help answer a variety of questions about how to work with data and analyses.)
Syllabus Psychology 301 Statistical Methods 3
• Fay, D. S., & Gerow, K. A biologist’s guide to statistical thinking and analysis. WormBook: the online review of C. elegans biology. http://www.wormbook.org/chapters/www_statisticalanalysis/statisticalanalysis.html (We include this as an example of a very condensed overview of basic statistics)
Assignment:
A common measure of intelligence is the intelligence quotient (IQ) test (Castles, 2012; Naglieri, 2015; Spinks et al., 2007) in which scores in the general healthy population are approximately normally distributed with 100 ± 15 (µ ± σ). Suppose we select a sample of 100 graduate students to identify if the IQ of those students is significantly different from that of the general healthy adult population. In this sample, we record a sample mean equal to 103 (M = 103). Compute the one-sample z test to decide whether to retain or reject the null hypothesis at a .05 level of significance (α = .05).” (Privitera 3rd Edition, page 250, Example 8.1). Use one or both of the following online calculators to answer this question:
* https://mathcracker.com/z-test-for-one-mean
* http://www.statskingdom.com/110MeanNormal1.html
Then, answer the following questions based on your results:
* What was the z-test statistic?
* Was it significant and how do we know?
* Using Cohen’s d-test to judge the effect size, calculate the value of Cohen’s d and interpret the outcome. Is the effect size small, medium, or large?
* Extending your knowledge: our sample size of 100 is fairly large. At what smaller sample size does the difference between the population mean of 100 and the sample mean of 103 become NOT statistically significant? Keep reducing the sample size in the calculator until you find out. Post that sample size here when you discover it. Explain how this does or does not change your thinking about the impact of sample size on significance testing.
* What is the difference between z-score and z-test?
Your main post should be at least 250 words with one reference.

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