# Hypothesis test regarding a standard deviation

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The annual temperature of a city is obtained by finding the mean of the mean temperatures on the 15th day of each month. The standard deviation of the annual temperatures of the city of a period of 100 years was 16 degrees Fahrenheit. During the last 15 years a standard deviation of annual temperatures was computed as 10 degrees Fahrenheit. Test the hypothesis that the temperatures in the city have become less variable than in the past, using a significance level of (a) 0.05 (b) 0.01.

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##### Solution Summary

This problem is a test of hypothesis comparing the variance (and standard deviation) of a new distribution with a known variance from another distribution. A step by step process is used, all formulas and calculations are shown and each step is explained.

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