# hw8 - 1 For a sample of 6 jugs of 2 low fat milk produced...

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1. For a sample of 6 jugs of 2 % low fat milk produced by “Happy Cow Dairy” the fat content X i has been determined as: 2 . 08 2 . 10 1 . 81 1 . 98 1 . 91 2 . 06 a) Making no assumptions on the distribution of the fat content, estimate the proportion of milk jugs having a fat content of 2.05 % or more. b) Estimate the mean fat content of “Happy Cow Dairy” 2 % low fat milk. c) Are the estimators used in a) and b) unbiased? d) Give the estimated standard errors of the estimators used in a) and b). d) Are there any alternative estimators for the parameters in a) and b), if you are given the information that the variable ”fat content” is normally distributed? If so, state the alternative estimators. 2. A random sample of 100 voters is selected and 65 of them are found to favor Candidate C. We want to find a confidence interval for the proportion of the voting population favoring Candidate C. (a) Give the relevant parameter that is to be estimated, and the point estimator and the estimate. (b) Check the appropriate conditions to see whether one can use a large sample confidence interval for the parameter in (a). (c) Find a 95% confidence interval for the parameter you stated in part (a).

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