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Hypothesis Tests for Population Means Section 10-4 Warm-Up http://goo.gl/forms/ICVv9pe7Bd Remember: Sampling Distribution of Means x x n Approximately Normal If population is normal If n30 (CLT) Use the z Test Statistic if is known and it’s a large sample z x n Assumptions: 1. SRS 2. Approx Normal – since n> 30 or pop is normal 3. Independent (10 * n) If population standard deviation is unknown or n<30: Use T-Distribution Use tcdf (beginning, end, df) Assumptions SRS Approximately Normal n< 30: Use t unless there are outliers or the data is really skewed. n30: Use t (if is unknown), data can be skewed Use boxplots to check for skewness Independent A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. At = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation is $5,230. A national magazine claims the average student watches less tv than the general public. The national average is 29.4 hours with a standard deviation of 2 hours. In a sample of 30, the mean is 27 hours. Using a confidence level of 0.01, is there enough evidence to support their claim? The average salary for nurses is $24,000. A sample of 10 nurses has a mean of $23,450 and a standard deviation of $400. Is this really the mean salary. Use = 0.05. A machine is designed to fill jars with 16 ounces of coffee. A consumer suspects that the machine is not filling the jars completely. They sampled 12 jars shown below. Is there enough evidence to support the consumer’s claim at = 0.10? 15 15.4 16.2 16.1 15.8 16.2 15.7 15.6 16 16.3 15.3 15.9 The Medical Rehabilitation Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. to see if the average cost of rehabilitation is different at a large hospital, a researcher selected a random sample of 35 stroke victims and found that the average cost of their rehabilitation if $25,266. The st. dev. Is $3,251. At = 0.01, can it be concluded that the average cost at a large hospital is different? A researcher wishes to test the claim that the average age of lifeguards is Ocean City is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7, with a st. dev. Of 2 years. Is there evidence to support the claim at = 0.05? A physician claims that jogger’s maximal volume oxygen uptake is greater than the average of all adults. A sample of 15 joggers has a mean of 43.6 ml per kg and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician’s claim at = 0.01?