Question

Use another random decimal fraction generator at Random.org, linked here, to generate a list of ten two-digit random numbers between 10 and 30. Calculate the z-score of the median of the data set.

• Set 1: 13, 14, 20, 21, 22, 24, 25, 26, 27, 30
• 
  What does the z-score of the data set median just above tell you about the shape of the distribution? How do you know this?

If you were to take repeated random samples of n = 5 from the data set just above, what would be the expected value of the mean of the sampling distribution of sample means?

Considering the set of ten two-digit random numbers above as a population, calculate the standard error of the mean for the samples in question 4.

Answer 1

Answer:

Use another random decimal fraction generator at Random.org, linked here, to generate a list of ten two-digit random numbers between 10 and 30. Calculate the z-score of the median of the data set.

• Set 1: 13, 14, 20, 21, 22, 24, 25, 26, 27, 30

n	10
mean	22.20
sample standard deviation	5.45

Median = 23

Z score for median = ( median-mean)/sd= (23-22.20)/5.45 = 0.146788991

=0.15 ( 2 devcimals)

What does the z-score of the data set median just above tell you about the shape of the distribution? How do you know this?

Positive z value tells that distribution is negatively skewed

If you were to take repeated random samples of n = 5 from the data set just above, what would be the expected value of the mean of the sampling distribution of sample means?

expected value of the mean of the sampling distribution of sample means is equal to mean value of data set, 22.20.

Considering the set of ten two-digit random numbers above as a population, calculate the standard error of the mean for the samples in question 4.

Standard error = sd/sqrt(n) = 5.45/sqrt(10) = 1.723