Question

All statistical tests are carried out at a =0.05. QUESTION ONE The following output represents data collected for the study of manpower allocation in the Ghana Police Service from various district across the country. The study involved testing the association among the key variables; comprising - Crimes (The number of reported crimes); Officers (The number of full-time equivalent police officers); Support (The number of civilian support staff); Unemployed (The unemployment rate); Retired (The percentage of the local population who are retired). Output: Table 1 Correlation Results of Key Variables Correlations Unemployme Crime Officers Crime Pearson Correlation - 763 Sig. (2-tailed) N 20 Officers Pearson Correlation Sig. 2-tailed) N Support Pearson Correlation Sig. (2-tailed) N Unemployment Pearson Correlation Sig. (2-tailed) 1 Support 454 .045 .000 20 1 - 434 .056 20 1 20 - 763 .000 20 454 .045 20 .748 .000 20 - 838 .000 20 nt .748 .000 20 - 460 041 20 254 280 20 Retired - 838 .000 20 .664 .001 20 - 350 .131 20 -610 .004 20 1 20 -434 .056 20 - 460 .041 20 664 .001 20 N 20 1 Retired 254 .280 20 - 350 131 20 Pearson Correlation Sig. (2-tailed) 20 -610 .004 20 N 20 Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed). a) Briefly explain correlation analysis and state the types of correlation. b) Formulate hypotheses to test the correlation between unemployment rate and crime. c) Perform a statistical analysis based on the output in Table 1 on the hypotheses you have formulated in (b). Clearly state your conclusion.

Answer 1

In each section we have for two variables correlation values, p-values and sample size.

a). For 5 variables, we have 5*5 matrix where we have correlation between each possible pair.

• A variable's correlation with itself is always 1 as one can see the diagonal
• Correlation > 0.7 is considered strong positive e.g., Crime vs unemployement, etc. They have influence on each other in same direction i.e, as one increases other increases.
• Correlation < -0.7 is considered strong negative e.g., Crime vs Officers, etc. They have influence on each other in opposite direction i.e, as one increases other decreases.

b). The correlation is 0.748

Hypothesis:

Ho: The correlation between Crime and Unemployment is not significant or $\rho_{Crime,Unemployment} = 0$

H1: The correlation between Crime and Unemployment is significant or $\rho_{Crime,Unemployment} \neq 0$

c). The correlation is 0.748 and p-value = 0.000 < 0.05 and 0.000<0.01 meaning that we reject Ho at alpha = 0.01 as well as 0.05. or we can say that correlation is significant at 5% or even 1%.

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