An IQ test was administered to twelve students and the scores were as follows:Student123456789101112IQ score87102948111575741169811496100Assume that IQ is normally distributed with mean m and variance .If =196, construct a 95% confidence interval for m, the true mean IQ in the population.What sample size is necessary to ensure an interval width w = 10? (Now consider Is the claim that m is less than 100 justified? Perform a test at the a = 0.10 level of significance, by the following 5 steps: Step 1. Hypotheses and significance level: H0: Ha: a =Step 2. Test Statistic and its sampling distribution under H0:Step 3. Observed value of the test statistic:Step 4. P-value under H0:Step 5. Decision and conclusion (interpretation of the result):

Name: An IQ test was administered to twelve students and the scores were as
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Description: An IQ test was administered to twelve students and the scores were as follows:Student123456789101112IQ score87102948111575741169811496100Assume that IQ is normally distributed with mean m and variance .If =196, construct a 95% confidence interval for

1) The mean and standard deviation is The confidence interval is 2) The width of the confidence…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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An IQ test was administered to twelve students and the scores were as follows:

Student	1	2	3	4	5	6	7	8	9	10	11	12
IQ score	87	102	94	81	115	75	74	116	98	114	96	100

Assume that IQ is normally distributed with mean m and variance .

If =196, construct a 95% confidence interval for m, the true mean IQ in the population.
What sample size is necessary to ensure an interval width w = 10? (
Now consider Is the claim that m is less than 100 justified? Perform a test at the a = 0.10 level of significance, by the following 5 steps:

Step 1. Hypotheses and significance level:

H₀: H_a: a =

Step 2. Test Statistic and its sampling distribution under H₀:

Step 3. Observed value of the test statistic:

Step 4. P-value under H₀:

Step 5. Decision and conclusion (interpretation of the result):

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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