The mean IQ for the entire population in any age group is known to be 100 with a standard deviation of 15. Suppose the IQ scores of 72 12th graders in Columbus are measured and the sample mean is found to be 103.4 and the sample standard deviation is 20.2. Do the scores provide good evidence that the mean IQ of this population is not 100?State the null (H0) and alternative (Ha) hypotheses.2. What are the confidence intervals for this data?3. What is the value of the test statistic?4. What is the p-value for this data?5. What is your decision about the null hypothesis?: Reject Fail to Reject6. Summarize the conclusion in the context of the problem.

The random variable IQ follows normal distribution. The population standard deviation is 15. The sample size is 72. The sample mean is 103.4. We have to test whether the mean IQ of this population is not 100 or not. This is one-sample z-test with two-tailed.Null Hypothesis: Alternative Hypothesis:From Z-table, the z-critical value at 95% level is 1.96. The 95% confidence interval is (99.935, 106.865).The value of the test statistic is z = 1.92.p-value = 0.0544.Since p-value (=0.0544) >α( 0.05), then fail to reject the null hypothesis.Conclusion: The scores do not provide good evidence that the mean IQ of this population is not 100.

Answered: The mean IQ for the entire population…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The mean IQ for the entire population in any age group is known to be 100 with a standard deviation of 15. Suppose the IQ scores of 72 12th graders in Columbus are measured and the sample mean is found to be 103.4 and the sample standard deviation is 20.2. Do the scores provide good evidence that the mean IQ of this population is not 100?