Question

Problem 5: [7 points) Let X equal the weight in grams of a 52-gram snack pack of candies. Assume that the distribution of X is N(41, O2). A random sample of n = 10 observations of X yield the following data: 55.95, 56.54, 57.58, 55.13, 57.48, 56.06, 59.93, 58.3, 52.57, 58.46. (a) Give a point estimate of Ji and o based on the data. [3] (b) Find the endpoints of a 95% confidence interval for J. [2] (c) Suppose now that X follows a N (1, 22). Repeat part b) and interpret the interval. [2]

Answer 1

Answer:-

point estimate of u is = Exi 3 56909 14 o mean 10 S S 2.0583 g . = 156177 : x = sample mean populatio point estimate of riss sample standard deviation Elxi-x)2 38:1298 hol point estimate of ris 2' 0583 ez 09818 T- GOOSE tceltical = tn-1,942 tg, a oslz 2.262 gs lo for u is (at tnitte slo) ( 5609 † 21262 x 200583/00) (56.19 t. 1.4723) +55+2994 58.2423) 55. 2977 58. 2423 are the end point confidence internal for e. xu hru, 82) 6=2 Cknown). use e test 24, - Zoof, |:36. ... 75% for el is (Z2/26/6) 56.97€ 1.96 x 2/50) (56.9 1.2396) (5505304 sfe 0096) are the end points of (1 for et Interpeet It say that we are 95% confident that the true population mean is lies between the end points of confidence internal 55. 5304 and 58.0036 and of

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