Hypothesis Testing for Standard Deviation or Variance

Testing a Claim about a Standard Deviation or VarianceWe first need to make sure we meet the requirements.1. The sample observations are a simple random sample.2. The population has a normal distribution.Test Statistic for Testing a Claim about a or .

Testing a Claim about orCritical-value method in 5 Steps1. State the hypothesis and state the claim. 2. Compute the test value. (Involves find the sample statistic). 3. Draw a picture and find Critical Values.4. Make the decision to reject or not. (i5. Summarize the results.

Testing a Claim about orWhen 40 people used the Weight Watchers diet for one year, their weights losses had a standard deviation of 4.9lb. Use a 0.01 significance level to test the claim that the amounts of weight loss have a standard deviation equal to 6.0lb, which appears to be the standard deviation for the amounts of weight loss with the zone diet.1. and

2. Critical value= 20.707 and 66.7663. Fail to reject since our test stat 26.011 is not in the critical

region.4. There is not sufficient evidence to warrant rejection of the

claim.

Testing a Claim about orA simple random sample of 30 men results in a standard deviation of 11.3 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation greater than 10 beats per minute.

Testing a Claim about orListed below are the playing times of songs that were popular at the time of this writing. Use a 0.05 significance level to test the claim that the songs are from a population with standard deviation less than one minute. 448 242 231 246 246 293 280 227 244 213 262 239 213 258 255 257