Please Complete The Following Step 1 Using Minitab Create 10

Please Complete The Followingstep 1 Using Minitab Create 100 Sample

Please complete the following: Step 1: Using Minitab, create 100 samples (c1-c100) of size 20 (i.e., 20 rows of data) from a Normal Distribution with a Mean = 100 and a Standard Deviation = 15. Why Mean = 100, and Sigma = 15? It's the Mean and Standard Deviation of the Wechsler IQ Test, which is one of the two "Gold Standard" IQ tests—the other being the Stanford-Binet.

Step 2: Perform a two-tail hypothesis test (using the 1-Sample Z option) on columns c1-c50. Enter a Standard Deviation of 15 and a Test Mean of 100.

Step 3: Place a '#' after any p-value less than 0.05.

Step 4: Perform a two-tail hypothesis test (using the 1-Sample Z option) on columns c51-c100. Enter a Standard Deviation of 15 and a Test Mean of 110.

Step 5: Place a '$' after any p-value greater than or equal to 0.05.

Paper For Above instruction

The purpose of this analysis is to generate simulated IQ data based on a well-known standard, perform statistical hypothesis testing, and interpret the results within the context of intelligence measurement. Using Minitab software, the first step involves creating 100 samples of size 20 each, drawn from a normal distribution with a mean of 100 and a standard deviation of 15. This distribution aligns with the characteristics of the Wechsler IQ test, a widely accepted measure of human intelligence, which has a mean score of 100 and a standard deviation of 15 (Wechsler, 2008).

Creating the samples in Minitab involves utilizing the "Random Data" generator feature. The process entails selecting the normal distribution option, entering the mean (100), standard deviation (15), and establishing 100 columns (c1 to c100), each with 20 rows. This simulation mimics the distribution of IQ scores within the general population, facilitating further statistical analysis.

Subsequently, hypothesis testing is employed to compare the sample means against a hypothesized population mean. The first set of tests targets columns c1 through c50, where a two-tailed z-test is conducted with the hypothesized population mean of 100 and a known standard deviation of 15. The z-test in Minitab checks whether the observed sample means significantly differ from the hypothesized mean, providing p-values indicative of statistically significant deviations.

Results from these tests are then analyzed: any p-value less than 0.05 (indicating statistical significance at the 5% level) prompts the placement of a '#' symbol beside the p-value. This notation highlights instances where the null hypothesis (that the sample mean equals 100) can be rejected, suggesting that the sample may reflect a true deviation from the hypothesized population mean.

The process continues with the second batch of samples, columns c51 through c100. Here, identical two-tailed z-tests are performed, but the hypothesized mean shifts to 110, reflecting a potential higher IQ score threshold. The same standard deviation of 15 is maintained to ensure consistency. After conducting these tests, any p-value greater than or equal to 0.05 is marked with a '$' symbol. This notation indicates the lack of statistically significant difference from the hypothesized mean of 110, supporting the null hypothesis in those cases.

This simulation and analysis provide insights into the variability and statistical significance of IQ scores based on randomly generated samples. It demonstrates how hypothesis testing can be applied to real-world standardized test data, such as IQ assessments, to evaluate whether observed sample means deviate meaningfully from expected population parameters.

References

  • Wechsler, D. (2008). Wechsler Adult Intelligence Scale–Fourth Edition (WAIS–IV). San Antonio, TX: Pearson.
  • Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486–489.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
  • Glass, G. V., & Hopkins, K. D. (1996). Statistical Methods in Education and Psychology. Prentice-Hall.
  • Levine, S. (2013). Understanding Hypothesis Testing. Harvard University Press.
  • Bluman, A. G. (2012). Elementary Statistics: A Step By Step Approach. McGraw-Hill Education.
  • Steinmetz, H. W., Gass, J. E., & Gallen, D. (2004). Statistical Methods for Psychology. Psychology Press.
  • Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression. Wiley.
  • McClave, J. T., & Sincich, T. (2018). Statistics (12th ed.). Pearson.

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