Question

A midsized university collected data on all 10,128 seniors attending. One variable of interest was how many credits they earned after they completed two years of school (i.e. credits they earned by their junior year).

a) Obtain the mean and standard deviation for the credits variable. Present the mean and standard deviation in one table and round the values to two decimal places. Are these calculations parameters or statistics? Answer this question in one sentence.

Column	Mean	Std. dev.
Credits	52.44	12.54

Are these calculations parameters or statistics? Answer this question in one sentence.

b) Take one sample of size 7 from the population and calculate the mean and standard deviation of this sample. Present the mean and standard deviation in one table and round the values to two decimal places. Are these calculations parameters or statistics? Answer this question in one sentence.

Column	Mean	Std. dev.
Sample 7 (Credits)	52.14	8.43

c) Does the sample mean calculated in (b) come from a normal sampling distribution? Check the three conditions of the Central Limit Theorem using one complete sentence for each condition.

d) Take one sample of size 28 from the population and calculate the mean and standard deviation of this sample. Are these calculations parameters or statistics? Answer this question in one sentence.

Column	Mean	Std. dev.
Sample 28 (Credits)	48.75	11.71

e) Does the sample mean calculated in (d) come from a normal sampling distribution? Check the three conditions of the Central Limit Theorem using one complete sentence for each condition.

Answer 1

(a) These calculations are parameters, because they have been calculated from the population, i.e., all 10,128 seniors attending the mid-sized university.
(b) These calculations are statistics, because they have been calculated from the sample of size 7 which was taken from the above-mentioned population.
(c) The sample has been sampled randomly from the population and its size is not more than 10% of the population, but the sample size is not large enough. So, the sample mean calculated in (b) does not come from a normal sampling distribution.
(d) These calculations are statistics, because they have been calculated from the sample of size 28 which was taken from the above-mentioned population.
(e) The sample has been sampled randomly from the population and its size is not more than 10% of the population. Also, the sample size is large enough. So, the sample mean calculated in (d) comes from a normal sampling distribution.