On the basis of this sample, can the researcher conclude that vocabulary skills for children with no siblings are significantly different from those of the general population

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A psychologist has developed a standardized test for measuring the vocabulary skills of 4-year-old children. The scores on the test form a normal distribution with μ = 72 and σ = 12. A researcher would like to use this test to investigate the idea that children who grow up with no siblings develop vocabulary skills at a different rate than children in large families. A sample of n = 25 children is obtained, and the mean test score for this sample is 66. On the basis of this sample, can the researcher conclude that vocabulary skills for children with no siblings are significantly different from those of the general population? Test at the .01 level of significance.

For each problem students will write out all steps of hypothesis testing:

  1. State the null and research hypotheses.
  2. Set the level of risk associated with the null hypothesis.
  3. Select the appropriate test statistic.
  4. Compute the test statistic value (called the obtained value).
  5. Determine the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic.
  6. Compare the obtained value and the critical value.
  7. Make your decision.
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