Sampling Distributions for Means

Worksheet 2 Solutions

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  1. a) the weight of Jiffy jars, quantitative b) all Jiffy jars; 32.3 and 0.40 are parameters,
    c) 32.3; NO-It's a parameter, d) 0.2266, e) 0.2266, f) a statistic, g) 32.3 and 0.1633,
    h) normal, i) 0.0329 j) 32.3, 0.0816, the standard deviation is one-half as large, k) 0+
  2. a) 0.2586 b) 0.9652 c) 0.9972
  3. a) The distribution is discrete (it is a count). It may have a little right skew. 0 is the minimum possible, 1.8 the mean, but the maximum possible could be quite high (5 murders in a year has some, even if a small, probability of occurring). b) 1.8, 0.671 c) 0.0099 d) The total exceeds 2.5*25 = 62.5.
  4. a) the b index of a stock on the NY Stock Exchange; it is quantitative, b) all stocks on the NY Stock Exchange; 1 and 0.26 are parameters, c) The distribution is right skewed,
    d) It is not possible to compute the probability: the shape is right skewed so you can't use a normal distribution; to find the value merely find the relative frequency of all stocks that have index above 1.15. e) It is a statistic; the parameter here is 1 = mean for all stocks, f) 1 and 0.058, g) 0.0051 (1 in 196), h) I do not choose the stocks at random: although a random selection could lead to my average exceeding 1.15, the answer to (g) shows that this is very unlikely. It is more reasonable to assume that my investment strategy involves choosing "riskier than average" stocks.