Question

For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 2 sentences.

a) The probability that a continuous random variable takes a specific value is 0.

b) Statistical inference is the process of drawing conclusions about unknown statistics by using known parameters.

c) The terms “histogram” and “bar graph” are synonyms.

d) If two events A and B are independent, then there is no overlap between the events on a Venn diagram.

e) The standard deviation of the number 10 is 1.

f) A weighted mean is preferred over an unweighted mean (i.e. a regular sample mean) when each observation has its own unique weight.

g) A z-score is a percentile.

h) Assuming the population is normally distributed, the standard deviation of the sampling distribution of the sample means will always be less than or equal to the population standard deviation.

i) If the sample size increases, but p stays the same, then the standard deviation of the sampling distribution of the sample proportion decreases.

j) Extreme values should always be excluded from subsequent analysis

Answer 1

e: standard deviation= square root (10) which is not equal to 1 so false.

f: simple mean is used when we associate equal weight to each observation on the other hand weighted mean is used when each observation is having different weight i.e. with each observation we associate unequal weight according to the importance of the observation.