a) Figure 3.5(a) shows sample proportions from samples of size n = 40 from a pop

Question

a) Figure 3.5(a) shows sample proportions from samples of size n = 40 from a population.

b) Figure 3.5(c) shows sample means from samples of size n = 100 from a population.

c) Figure 3.5. Several possible values are given for a sample statistic. In each case, indicate whether each value is (i) reasonably likely to occur from a sample of this size, (ii) unusual but might occur occasionally, or (iii) extremely unlikely to ever occur. 3.16   Using the sampling distribution shown in Figure 3.5(a), how likely are these sample proportions:

(a)

(b)  

(c)

d) Using the sampling distribution shown in Figure 3.5(c), how likely are these sample means:

1) x=250

2) x=305

3) x=315

Exercises 3.12 to 3.15 refer to the sampling distributions given in Figure 3.5. In each case, estimate the value of the population parameter and estimate the standard error for the sample statistic. 0.02 0.09 0.16 0.23 0.30 0.37 0.44 0.51 0.58 25 45 65 85 105 125 145 285 290 295 300 305 310 315 0.71 0.74 0.77 0.80 0.83 0.86 0.89 Figure 3.5 Four sampling distributions

Explanation / Answer

d>this is apparently a normal distribution, so generally chances of getting values from the middle is higher than getting values at the edges relative to the curve.
1. x=250 :extremely unlikely to ever occur. as the values is at extreme end relative to the distribution curve.

2.x=305: reasonably likely to occur from a sample of this size. we observe that the 300 is more or less the mean median and mode of the graph and 305 is close to 300 so getting 305 is reasonably likely.

3.x=315: unusual but might occur occasionally

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