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.

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 mean 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

f) TRUE

REASON: A weighted mean is preferred over an unweighted mean because the final average number reflects the relative importance of each observation and is thus more descriptive than a simple average.

g) FALSE

REASON: A z-score is not a percentile because a z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units.

h) TRUE

REASON: The sample variance is more often less than the population variance due to the skewed nature of the distribution of the unbiased sample estimate.

i)TRUE

REASON: Because with bigger sample sizes, the sample mean becomes more accurate estimate of the parametric mean, so the standard deviation of the sampling distribution of the sample proportion decreases.