### Educational Transcription for Website---**Question:**a. Conduct a two-tailed test to determine if the population mean is equal to \( \mu = 100 \). Use \( \alpha = 0.01 \).b. Construct an 80% confidence interval estimate for today's population mean IQ for the 10-year-old test.**Notes:**- Remember to refer to the necessary statistical tables to find critical values.- Make use of standard formulas for hypothesis testing and constructing confidence intervals.No graphs or diagrams are provided with this text.---### Explanation:This task requires performing a two-tailed hypothesis test as well as constructing a confidence interval. The hypothesis test uses a significance level (\( \alpha \)) of 0.01, and the confidence interval is constructed at an 80% confidence level.1. **Hypothesis Test:** - Null Hypothesis (\( H_0 \)): \( \mu = 100 \) - Alternative Hypothesis (\( H_a \)): \( \mu \neq 100 \) - Use the given \( \alpha \) value to find the critical values from the appropriate statistical table (z-table or t-table, depending on sample size and standard deviation information).2. **Confidence Interval:** - Calculate the sample mean and standard deviation if not provided. - Use the formula for the confidence interval: \[ \text{CI} = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \] - Determine the Z-value corresponding to 80% from the Z-table. **Further Learning:**For more detailed instructions on hypothesis testing and confidence interval calculations, see the tutorial sections on statistical hypothesis testing and confidence intervals. ### The Flynn Effect and IQ TestingFor several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the researcher who first reported it (Flynn, 1984, 1999), and it means that psychologists must continuously update IQ tests to keep the population mean at μ = 100. To evaluate the size of the effect, a researcher obtained a 10-year-old IQ test that was standardized to produce a mean IQ of μ = 100 for the population 10 years ago. The test was then given to a sample of n = 64 of today's 20-year-old adults. The average score for the sample was M = 107 with a standard deviation of s = 12.#### Statistical Analysis**a.** Based on the sample, is the average IQ for today’s population significantly different from the average 10 years ago, when the test would have produced μ = 100? ---#### Steps for Hypothesis Testing1. **State the Hypotheses:** - Null Hypothesis (H₀): The average IQ for today's population is 100 (no difference). - Alternative Hypothesis (H₁): The average IQ for today’s population is not equal to 100 (significant difference).2. **Set the Significance Level:** - Use a significance level of α = 0.01.3. **Calculate the Test Statistic:** - Use an appropriate statistical test (e.g., t-test) to compare the sample mean to the population mean.---This examination of IQ scores helps to understand the implications of the Flynn effect and the necessity for periodic updates in IQ testing to accurately reflect the current population's intellectual abilities.

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The null and the alternative hypotheses are, H0: µ=100 HA: µ≠100 Test statistic: Thus, the test…

Math

Statistics

For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenom- enon is called the Flynn effect after the researcher 00) and it

For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenom- enon is called the Flynn effect after the researcher 00) and it

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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