Introduction to Statistics Study

Sampling and Sampling Distributions 

Question one

Population mean: 

Population Standard Deviation: 

1.  

Random sample #1: 3, 4, 9

Random sample #2: 2, 3, 12

Random sample #3: 3,7,8

1.  

Random sample #1: Mean:  Standard Deviation: 

Random sample #2: Mean:  Standard Deviation: 

Random sample #3: Mean:  Standard Deviation: 

1.  

Random sample #1: 

Random sample #2: 

Random sample #3: 

Random sample #3

Random sample #1

Mean of the sampling distribution: 

1.  

Standard error of the mean

To make it a better approximation, we could increase the size (n) of the sample.

Estimation 

Question one

Confidence interval formula

Calculating 95% confidence interval for the mean number of years of education for lower-class respondents.

Upper bound

Lower bound

99% confidence interval

Upper bound

Lower bound

95% confidence interval for the mean number of years of education for middle-class respondents

Upper bound

Lower bound

99% confidence interval

Upper bound

Lower bound

80% confidence interval for the mean number of years of education for working class respondents

Upper bound

Lower bound

90% confidence interval

Upper bound

Lower bound

80% confidence interval for the mean number of years of education for upper-class respondents

Upper boundary

Lower boundary

90% confidence interval

Upper boundary

Lower boundary

As our confidence in the result increases, the size of the confidence interval increases so to increase the probability of the population mean being found within the interval.

Question 2

1.  

Upper boundary

Lower boundary

Yes, the confidence interval is meaningless. This is because any other distribution other than a normal distribution skewed in whichever way does not provide for the appropriate rejection region and therefore the results of the confidence interval become meaningless.