Consider two experiments. First, from a population that is normally distributed
ID: 3200182 • Letter: C
Question
Consider two experiments. First, from a population that is normally distributed with mean 10, we select one item and find its weight. Let D1 be the distribution of possible outcomes from experiment 1. Second, we take a sample of 5 items from the same population and calculate the average weight of the 5 items. Let D2 be the distribution of possible outcomes (sample averages) resulting from experiment 2. Which of the following statements is true and which is not true?
Statement True or False? 1. D1 is narrower than D2 2. D1 and D2 are both normally distributed. 3. D1 and D2 have the same spread (standard deviation) 4. D1 and D2 have the same mean. 5. D1 is wider than D2Explanation / Answer
Solution:
Statement
True or False?
Both the distribution is drawn from the normal distribution so both would be normally distributed.
Distribution drawn from a same population have same mean.
Distribution drwn from the same population cannot have same spread beacuse spread depends upon the sample size.
As the sample size increases the spread decreases and when the sample size decreases the spread increases therefore D1 is wider than D2
Statement
True or False?
1. D1 is narrower than D2 FALSE 2. D1 and D2 are both normally distributed. TRUE 3. D1 and D2 have the same spread (standard deviation) FALSE 4. D1 and D2 have the same mean. TRUE 5. D1 is wider than D2 TRUE