After randomly sampling the population, we get that P-value< α = 0.05 so, rejected the null hypothesis. Therefore we can conclude that there is a significant relationship between democracy and wars.
A study about a state being a democracy influences how many wars it's had over the last 100 years. For hypothesis testing, consider the null and alternative hypothesis being tested is:
H₀ : μ₁ = µ₂
Hₐ : µ₁ ≠ µ₂
Demo Non-demo (wars)
4 7
7 9
3 12
4 15
6 20
Mean for demo wars , X₁-bar = 4.8
Mean for Non-demo wars , X₂-bar = 12.60
Standard deviations for demo wars, s₁
= 1.64
Standard deviations for no-demo wars, s₂
= 5.13
Sample size, n₁ = n₂ = 5
degree of freedom, df = n₁ + n₂ - 2 = 10 - 2
=8
Mean difference (Demo - Non-demo)
= -7.800
Significance level, α = 0.05
Pooled variance ,
= √((n₁-1)s₁² + (n₂-1)s₂²)/n₁+n₂-2) = 14.500
Pooled std. dev. = 3.808
Standard error of difference, S.E
= 14.50/3.808 = 2.408
Hypothesized difference = 0
This is the formula we really use for the t-score.
t =( X₁-bar - X₂-bar)/S.E = -7.800/2.408
= -3.239
Using the t-statistic table, p-value (two-tailed) for t = -3.239 and 8 degree of freedom is 0.0119. Since the p-value (0.0119) is less than the significance level (0.05), we can reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between democracy and wars.
To learn more about Hypothesis testing, refer:
https://brainly.com/question/4232174
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Complete question:
Let's say that we're interested in whether a state being a democracy influences how many wars it's had over the last 100 years. After randomly sampling the population, we get the following.
Democracies a b c d e
Wars 4 7 3 4 6
Non-demo e f g h i
Wars 7 9 12 15 20
Based on these data, is there significant relationship between democracy and wars? Run some test to figure this out, and be sure to show your work.
