homework_8_ans_stud

# homework_8_ans_stud - Course MTH 1210 Apr 1609...

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Course MTH 1210 Apr 16’09 Homework #8 ( answers ) ( Confidence intervals for a population mean with t statistic ) Use MS Excel program Sampling distribution of sample means.xls, sheet 3 (block of cells I6 L9 ) and the formula for the confidence interval (see Handout #10) _ _ _ _ _ _ x * ± t (1 – α/2) s/√n or [ x * – t (1 – α/2) s/√n , x * + t (1 – α/2) s/√n ] (10.4) _ where x * and s are a sample mean and a sample standard deviation, respectively, n is a sample size , t (1 – α/2) is the reliability factor (coefficient) to solve the problems below. 1. {problem 6.3.1, pg. 171 Biostatistics} Use the t distribution to find the reliability factor t (1 – α/2) for a confidence interval based on the following confidence coefficients 1 – α and sample size n : a b c d ---------------------------------------------------------------------- 1 – α | 0.95 | 0.99 | 0.90 | 0.95 | ---------------------------------------------------------------- n | 15 | 24 | 8 | 30 | ====================================== α | 0.05 | 0.01 | 0.1 | 0.05 | J9 ---------------------------------------------------------------- n – 1 | 14 | 23 | 7 | 29 | J8 ---------------------------------------------------------------- t (1 – α/2) | 2.144787 | 2.807336 | 1.894579 | 2.04523 | L9 [ t (1 – α/2) ] ALLWAY N-1 (1- α) =.95 α= 1-0.95 X=.05 2. {problem on pg. 318 of Elementary Statistics book} A random sample of size 20 is taken from the weights of babies born at some hospital in 1979. A mean of 6.87 pounds and a standard deviation of 1.76 pounds were found for the sample. Estimate, with 95% confidence, the mean weight of all babies born in this hospital in 1979 year.

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