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?

1. 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 Reject

6. Summarize the conclusion in the context of the problem.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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