Data Analysis, please show all workThe amount of yearly rainfaill in Chicago was sampled. 40 years from the records was randomly checked. The mean rainfaill was 33.98 in ches, with a standard deviation of 5.22 inches.Provide 90%, 95%, and 99% confidence intervals for these values. Remember to provide your answer in the form of a properly phrased confidence interval statement.Suppose the sample size was doubled. How would this affect the confidence interval? You don't have to provide a quantitative answer here. Simply indicate if it would go up, down, or remain approximately the same.

Confidence interval is the range used to determine where the population mean lies. It varies based on the confidence interval. If the confidence level increases, the range become tighter or close. If the confidence interval decrease, the range become wider. a) Given : Amount of yearly rainfall in Chicago was sampled. Sample size is 40 Mean rainfall is 33.98 inches Standard deviation of rainfall is 5.22 inches Confidence interval at 90% : z critical value at 90% is 1.65 (From z table) Now, x¯±z0.10×σn=33.98±1.65×5.2240=33.98±1.36=33.98-1.36,33.98+1.36=32.62,35.34 The true population mean lie at the 90% confidence interval at the range 32.62 and 35.34 Confidence interval at 95% : z critical value at 95% is 1.96 (From z table) Now, x¯±z0.05×σn=33.98±1.96×5.2240=33.98±1.62=33.98-1.62,33.98+1.62=32.36,35.60 The true population mean lie at the 95% confidence interval at the range 32.36 and 35.60 Confidence interval at 99% : z critical value at 99% is 1.58 (From z table) Now, x¯±z0.01×σn=33.98±2.58×5.2240=33.98±2.13=33.98-2.13,33.98+2.13=31.85,36.11 The true population mean lie at the 99% confidence interval at the range 31.85 and 36.11b) Given : Let the sample size was double. If the sample size increases, the margin of error decreases. If the margin of error decreases, the closer the confidence interval range. Hence, the sample size increases the confidence interval range become small or go down.

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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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Data Analysis, please show all work

The amount of yearly rainfaill in Chicago was sampled. 40 years from the records was randomly checked. The mean rainfaill was 33.98 in ches, with a standard deviation of 5.22 inches.

Provide 90%, 95%, and 99% confidence intervals for these values. Remember to provide your answer in the form of a properly phrased confidence interval statement.
Suppose the sample size was doubled. How would this affect the confidence interval? You don't have to provide a quantitative answer here. Simply indicate if it would go up, down, or remain approximately the same.

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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