Question

A researcher claims that the number of homicide crimes by season is uniformly distributed. To test this​ claim, you randomly select 1 comma 187 homicides from a recent year and record the season when each happened. The table shows the results. At alpha ​= 0.05 ​, test the​ researcher's claim. Season ​Frequency, f Spring 300 Summer 310 Fall 292 Winter 285

Answer 1

1. State the hypotheses.

H0: The number of homicide crimes by season is uniformly distributed
H1: The number of homicide crimes by season is not uniformly distributed

2. Formulate an analysis plan.

For this analysis, let the significance level be 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

3. Analyze sample data.

Expected count for seeds under each seasom if null hypothesis is true, Ei = n * pi where pi = 1/4 for i = 1, 2, 3, 4

Ei = 1187 * 1/4 = 296.75   for i = 1, 2, 3, 4

Chi-square test statistic =

= 1.1685

Degree of freedom = k-1 = 4-1 = 3

P-value = P( > 1.1685) = 0.7606

4. Decision

Since P-value is greater than alpha = 0.05, we fail to reject the null hypothesis.

5. Conclusion

There is no sufficient evidence from the sample data to reject the researcher's claim that number of homicide crimes by season is uniformly distributed.