Question

1. True or False.

1a. z-scores follow a standard normal distribution.

1b. A z-score indicates how many standard deviations a value is 1b. above or below the mean.

1c. Point estimators are always good estimates of population parameters, and there are never any deviations or errors

1d. The process of converting a value x from a normal distribution to a z-score is known as standardization

Answer 1

1)

a) False. z-scores need not follow a standard normal distribution.Their mean is zero and s.d =1 . But there distribution depends on the underlying distrubtion of X from which the z-scores are calculated.

b) True. z-score denote how many s.tandard deviations is an observation above or below the mean. As

c) False. Point estimators as all other estimators are random variables and follow a sampling distribution.  Hence there will always be deviations and errors.

d) True. if X~ N() then z-score z, ~ N(0.1) and this process is called Standardization.