Question

There are 2 data sets below, choose which statistic to use and conduct your analysis . This is
completely up to you but note that your data will dictate what test you will run (see the book for examples and then compare to the examples below). Be creative and thorough in your analysis. I will expect 2 write-ups for both data sets.

Note: You will again need to use the tables in the back of the book to determine significance. Which table will be determined by which statistic you choose to use.

Project A: Assess the differences between Southerners and Non-Southerners on Church Attendance per Month. Below are number of days per month attended by South and non-South residents.

South             NonSouth
16                    8
13                    5
12                    4
15                    8
11                    1

Project B: Assess attitudes toward same-sex marriages of non-politician republicans and democrats
Note: 0=disagree with same-sex marriages and 10 = Agree with same-sex marriages

Republicans        Democrats      Independent
6                               8 6
5                             6                             7
3                                 9 5
7                                 8                             6
4                                 7                             5

Answer 1

PROJECT -A:

Here we have two independent samples so we used here two independent t-test

using Minitab software

Hypothesis:

H0: south and nonsouth church attendance are equal

H1: south and nonsouth church attendance are not equal

Two-Sample T-Test and CI: south, nonsouth

Two-sample T for south vs nonsouth

N Mean StDev SE Mean
south 5 13.40 2.07 0.93
nonsouth 5 5.20 2.95 1.3

Difference = μ (south) - μ (nonsouth)
Estimate for difference: 8.20
95% CI for difference: (4.39, 12.01)
T-Test of difference = 0 (vs ≠): T-Value = 5.09 P-Value = 0.001 DF = 7

here 0.001<0.05 so we reject null hypothesis so we say that there is a statistical significant difference between south and non south church attendance per month

Conclusion: There are differences between Southerners and Non-Southerners on Church Attendance per Month.

PROJECT: B

For this given data this data does not follow normality and also this data is the rank of data so we used a here nonparametric test KRUSKAL WALLIS TEST. it is similar to ANOVA.

using Minitab software

Hypothesis

H0: The means of all groups are equal

H1: Not all the means are equal

Kruskal-Wallis Test: C2 versus C1

Kruskal-Wallis Test

C1 N Median Ave Rank Z
Democrats 5 8.000 12.1 2.51
Independent 5 6.000 6.8 -0.73
Republicans 5 5.000 5.1 -1.78
Overall 15 8.0

H = 6.67 DF = 2 P = 0.036
H = 6.90 DF = 2 P = 0.032 (adjusted for ties)

here both p-value <0.05 so we reject the null hypothesis and say that all means are not equal

Conclusions: Attitudes toward same-sex marriages of non-politician republicans and democrats are different