Question

data set

West	SouthEast	MidWest	NewEngland
4	3	2	3
7	2	2	3
8	4	8	4
3	2	9	8
4	8	10	7
4	3	12	3
4	5	1	5
5	6	9	6
6	2	9	2
10	4	3	2
9	3	6	1
7	3	5	4
7	9	6	3
4	2	4	3
3	3	4	5
2	1	4	10
1	2	4	10
2	1	2	9
3	2	2	11
9	2	1
	1	1
	1
	3
	2

Part 1
Using the same data set, analyze the data for Midwest region. Do the following:
(1) Obtain a histogram and boxplot for the data (revisit one of the earlier lab reports).
(2) You need to test whether the mean number of years of education in this region is significantly different from 5.5. State the hypotheses.
(3) Perform an appropriate test of hypotheses; copy and paste the results.
(4) Identify the test statistic and the p-value, and state the decision.
(5) Interpret the p-value (see Week 5 module), and answer the research question.

Part 2
Using the same data set, consider the data for Southeast and West regions. Do the following:
(1) You need to test whether there is a significant difference in the mean number of years of education beyond high school between the two regions. State the hypotheses.
(2) Perform an appropriate test of hypothesis; copy and paste the results.
(3) Identify the test statistic and the p-value, and state the decision.
(4) Interpret the p-value (see Week 5 module), and answer the research question.
(5) Identify the 95% confidence interval for the mean difference, and interpret the result. How does this result relate to the results in parts (3) and (4) Be specific.

Support your conclusion with specific calculations.

Answer 1

Solution:

Part 1.

The histogram for Mid West is the following:

The boxplot for the MidWest is the following:

The null hypothesis is: Mean number of years of education in the Mid West region is equal to 5.5.

The alternative hypothesis is: Mean number of years of education in the Mid West region is different from 5.5.

We perform the test and have the following results tabulated below:

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
Mid_West	21	4.9524	3.35375	.73185

One-Sample Test
	Test Value = 5.5
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
Mid_West	-.748	20	.463	-.54762	-2.0742	.9790

Here the P-value is = 0.463>0.05, hence we fail to reject the null hypothesis.

Part2.

The null hypothesis is: Mean number of years of education beyond high school between the South East and West regions are equal.

The alternative hypothesis is: Mean number of years of education beyond high school between the South East and West regions are different.

We perform two independent sample t-test and obtain the following result:

Group 1 = West

Group 2 = SouthEast