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2010 Sample Final Key

# 2010 Sample Final Key - [SAMPLE TEST AMS110.02 Final...

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[SAMPLE TEST] AMS110.02 Final Exam (Spring 2010) Possible Points:100; Time: 120 Minutes Last Name: _____________________ First Name: _____________________ Student ID Number: _____________________ 1. A consumer watchdog group suspects that a yogurt that is advertised to be 98% fat free has in fact a higher mean fat content. The group will take action against the company if it can substantiate its suspicion with factual data. For this purpose, the group takes a sample of 25 yogurt cups (each containing 170 grams) and measured the fat contents. If the company’s claim is correct, then the mean fat content should be no more than 2%, i.e., 3.4 grams. Also suppose that σ of the fat contents is .5 grams. a. Set up the hypotheses to be tested. 0 : 3.4 : 3.4 a H versus H μ μ b. Suppose that the mean fat content for 25 sample cups was 3.6 grams. Report the p- value. 0 0 0 0 0 0 0 3.6, 25; .5; 3.4 3.6 3.4 .2 2 .1 / .5 / 25 ( ) ( 2) 1 ( 2) .0228 x n x z n P value P Z z P Z P Z σ μ μ σ = = = = - - = = = = - = = = - < = c. Is there enough statistical evidence to support the consumer group’s suspicion at .06 α = ? Explain using the p-value that you find. 0 .0228 .06 .06. P value Reject H at the significance level α α - = < = = 2. The length of human pregnancies from conception to birth varies. According to a study, its distribution approximates a normal distribution with mean of 280 days and standard deviation of 25 days. Suppose the length of a pregnancy of a woman is independent of the length of another pregnancy of the same woman at a different time.

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