Question

1. What does the z-score (-0.0566) of the data set (12, 14, 17, 19, 20, 21, 24, 25, 26, 30) median (20.5) just above tell you about the shape of the distribution? How do you know this? Expert Answer An expert answer will be posted here Post a question Answers from our experts for your tough homework questions

2. 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?

3. 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 2

Answer 1

1. Given data set

12, 14, 17, 19, 20, 21, 24, 25, 26, 30

Here n=10,

Mean = 20.8

Median = 20.5

Z-score = -0.0566

Standard deviation = 5.5936

Z- score for median = (median - mean)/standard deviation

= (20.5-20.8)/5.5936

= -0.0536

Negative z value tells that distribution is positively skewed

2. If you were to take repeated random samples of n = 5 from the data set just above, expected value of the mean of the sampling distribution of sample means is equal to mean value of data set, 20.8.

3. The standard error of the mean for the samples in question 2 is

Standard error = sd/sqrt(n)

= 5.5936/√10

= 1.7688