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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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):

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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