please use the calculator method The scores on the Wechsler Intelligence Scale for Children (WISC) arenormally distributed with a standard deviation of sigma - 10. A SRS of 25 children from Southwest Virginia is taken to determine the mean mew of all children from Southwest Virginia. If the mean of this sample is 104.32, find a 95% confidence interval for. What is the margin of error for this interval? ### Some Common Values of Z*This table provides values of Z* corresponding to different confidence levels, commonly used in statistical analysis for constructing confidence intervals. The Z* values are crucial for determining the margin of error in statistical estimates.| **Confidence Level** | **Tail Level** | **Z*** ||---------------------|---------------|--------|| 60% | 0.20 | 0.84 || 80% | 0.10 | 1.28 || 90% | 0.05 | 1.645 || 95% | 0.025 | 1.96 || 96% | 0.02 | 2.05 || 98% | 0.01 | 2.33 || 99% | 0.005 | 2.576 |### Explanation- **Confidence Level**: This indicates the percentage of all possible samples that can be expected to include the true population parameter. For example, a 95% confidence level means that we can be 95% certain that the true parameter is within our interval estimate.- **Tail Level**: The probability in each tail of the normal distribution that is not included in the confidence interval. It is calculated as (1 - Confidence Level)/2. For a 95% confidence level, the tail level is 0.025.- **Z* Value**: The Z-score, representing the number of standard deviations a data point is from the mean. It acts as a multiplier for the standard error in interval calculations. For instance, a Z* of 1.96 at 95% confidence level means the data point is 1.96 standard deviations away from the mean in a normal distribution.These values help in determining how wide the confidence interval around a sample statistic should be, thereby giving an indication of the precision of the estimate.

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MATLAB: An Introduction with Applications

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please use the calculator method

The scores on the Wechsler Intelligence Scale for Children (WISC) are

normally distributed with a standard deviation of sigma - 10. A SRS of 25 children from Southwest Virginia is taken to determine the mean mew of all children from Southwest Virginia. If the mean of this sample is 104.32, find a 95% confidence interval for. What is the margin of error for this interval?

### Some Common Values of Z*

This table provides values of Z* corresponding to different confidence levels, commonly used in statistical analysis for constructing confidence intervals. The Z* values are crucial for determining the margin of error in statistical estimates.

| **Confidence Level** | **Tail Level** | **Z*** |
|---------------------|---------------|--------|
| 60% | 0.20 | 0.84 |
| 80% | 0.10 | 1.28 |
| 90% | 0.05 | 1.645 |
| 95% | 0.025 | 1.96 |
| 96% | 0.02 | 2.05 |
| 98% | 0.01 | 2.33 |
| 99% | 0.005 | 2.576 |

### Explanation

- **Confidence Level**: This indicates the percentage of all possible samples that can be expected to include the true population parameter. For example, a 95% confidence level means that we can be 95% certain that the true parameter is within our interval estimate.

- **Tail Level**: The probability in each tail of the normal distribution that is not included in the confidence interval. It is calculated as (1 - Confidence Level)/2. For a 95% confidence level, the tail level is 0.025.

- **Z* Value**: The Z-score, representing the number of standard deviations a data point is from the mean. It acts as a multiplier for the standard error in interval calculations. For instance, a Z* of 1.96 at 95% confidence level means the data point is 1.96 standard deviations away from the mean in a normal distribution.

These values help in determining how wide the confidence interval around a sample statistic should be, thereby giving an indication of the precision of the estimate.

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 + ...

Expert Solution

Step 1

Confidence Interval

$l_{1} = X - t_{α} (S . E . o f X) - L o w e r l i m i t l_{2} = X + t_{α} (S . E . o f X) - U p p e r l i m i t$

given in the question $σ$ = 10, n=25 , $X = 104 . 32$ ,

$t_{α}$ at 5% level of significance = 1.96

S.E. of $X$

$= \frac{σ}{\sqrt{n}} = \frac{10}{\sqrt{25}} = 2$

Confidence interval

$l_{1} = 104.32 - 1.96 (2) = 100.4 l_{2} = 104.32 + 1.96 (2) = 108.24$

Hence the confidence interval would be-

(100.4< P < 108.24)

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