The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α = 0.01? Assume the amount of summer rainfall follows a normal distribution. Please also state if the assumption of normal distribution was essential for solving this question. You will need to specify the appropriate hypothesis, identify the statistical test, estimate p-value (using R command), and state your conclusion in the context of the problem. For the conclusion, please use the following template. If you reject the null write Since p-value is [write the value of your p-value] and is less than [write the value of alpha in percent] we reject the null hypothesis at [write the value of alpha]% significance level. That is, there is sufficient evidence in the data to reject [write down the null hypothesis in the context of the problem] If you fail to reject the null write Since p-value is [write the value of your p-value] and is greater than [write the value of alpha in percent], we fail to reject the null hypothesis at [write the value of alpha]% significance level. That is, there is not sufficient evidence in the data to reject [write down null in the context of the problem]

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α = 0.01? Assume the amount of summer rainfall follows a normal distribution. Please also state if the assumption of normal distribution was essential for solving this question.

You will need to specify the appropriate hypothesis, identify the statistical test, estimate p-value (using R command), and state your conclusion in the context of the problem.

For the conclusion, please use the following template.

If you reject the null write
Since p-value is [write the value of your p-value] and is less than [write the value of alpha in
percent] we reject the null hypothesis at [write the value of alpha]% significance level.
That is, there is sufficient evidence in the data to reject [write down the null hypothesis in the
context of the problem]

If you fail to reject the null write
Since p-value is [write the value of your p-value] and is greater than [write the value of alpha in
percent], we fail to reject the null hypothesis at [write the value of alpha]% significance level.
That is, there is not sufficient evidence in the data to reject [write down null in the context of the
problem]

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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