- 2.A researcher\'s sample of size n is to be selected from a population of inte

Question

- 2.A researcher's sample of size n is to be selected from a population of interest. Let Xi, ,x, represent the X measurements to be taken on these n individuals. Further, let X1m,... Xmm be the order statistics of the sample measurements and Zin..Znn their standardized values, that is, Ztn is the number of population standard deviations Xin is from the population mean. The ordered standardized value Zin varies over all possible researcher's samples. Hence, it has a distribution and this distribution has a mean, we will denote by '". The values 1m ,6,n are referred to in the literature as "plotting positions" when considering a plot of the points (6, Xi.), , (o,n,X Under the assumption that the measurements Xi.X, is a "random sample" with a common normal distribution, the plot of these points is called a probability plot. (A) exponential (B) Fisher (C) Deming (D) normal 3. (continuation) Under the assumption the X measurement has a normal distribution, then the points ( ",Xin), , (6,"'X,") will plot randomly about a line sloping upward to the right. If the researcher makes a subject judgement that the plotted points do not appear to plot randomly about a line sloping upward to the right, then the rescarch is rejecting the assumption that the X measurement has adistribution. (A) exponential (B) Fisher (C) Deming (D) normal 4. (continuation) When n-45, the TI-83 calculator approximates 3 45 as (A)-2.286548 (B)-1.593219 (C) 1.593219 (D) 2.286548 rounded to six decimal places.

Explanation / Answer

2. D) normal probability plot

3. D) normal distribution

4. The sample mean follows N(0,1/45)

2.286548

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