### Hypothesis Testing: Mean Full Scale IQ Score of Smart County Residents#### b. What are the null and alternative hypotheses? - $ \text{H}_0: \mu = 105; \text{H}_a: \mu \neq 105 $ - $ \text{H}_0: \mu = 105; \text{H}_a: \mu > 105 $ - $ \text{H}_0: \mu = 105; \text{H}_a: \mu \neq 100 $ - $ \text{H}_0: \mu = 100; \text{H}_a: \mu > 100 $#### c. What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average? - $ 0.333 $ - $ -0.333 $ - $ 3.33 $ - $ -3.33 $#### d. After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the P-value of 0.0004 was obtained. Use $ \alpha = 0.05 $. - Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average. - Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average. - Reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average. - Reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average. ### Educational Content: Hypothesis Testing for IQ Scores---**Understanding the Wechsler Adult Intelligence Scale (IQ Test)**The Wechsler Adult Intelligence Scale (IQ test) is constructed such that Full Scale IQ scores follow a normal distribution. This normal distribution has a mean of 100 and a standard deviation of 15. ### Case Study: Smart County's IQThe mayor of Smart Town believes the county's residents are smarter than the national average and wants to use this (the intelligence of the residents) as a marketing tool to attract industries to the area.A researcher has been hired to conduct a study to determine whether Smart County's residents have, on average, higher Full Scale IQs than the population.**Study Details:**- A random sample of 100 people from Smart County were given the IQ test.- The results showed an average Full Scale IQ of 105.### Hypothesis TestingThe researcher needs to determine whether the average IQ in Smart County is significantly higher than the national average. This calls for a hypothesis test.**Question:**Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?Here are the options:- $ \circ $ z-test for the population mean- $ \circ $ t-test for the population mean- $ \circ $ z-test for the population proportion- $ \circ $ t-test for the population proportion**Explanation:**- **z-test for the Population Mean:** This test is appropriate when the sample size is large (n > 30), and the population standard deviation is known.- **t-test for the Population Mean:** This test is used when the sample size is small and/or the population standard deviation is unknown.- **z-test for the Population Proportion:** Used for testing proportions, not means.- **t-test for the Population Proportion:** Also used for testing proportions, not means.Given that the sample size is 100 (which is greater than 30), and assuming the standard deviation of the population is known (standard deviation = 15 from the description), the appropriate test to use in this scenario is:### Answer:- $ \circ $ **z-test for the population mean**This choice is ideal for testing whether the mean Full Scale IQ score of the Smart County residents is significantly higher than the national average of 100.---**Graphical Representation

The population standard deviation is 15.

The Wechsler Adult Intelligence Scale (IỌ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county's residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. A researcher is hired to conduct a study to determine whether Smart County's residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105. a. Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?

The Wechsler Adult Intelligence Scale (IỌ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county's residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. A researcher is hired to conduct a study to determine whether Smart County's residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105. a. Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?

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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