A study was conducted to compare the mean numbers of police emergency

Question

A study was conducted to compare the mean numbers of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions and the number of emergency calls was recorded for each shift. The sample statistics are listed here:

	Region
	1	2
Sample size	100	100
Sample mean	2.4	3.1
Sample variance	1.44	2.64

Find a 90% confidence interval for the difference in the mean numbers of police emergency calls per shift between the two districts of the city. Interpret the interval.

20 Feb 2025

Answer :

Word Count : 340

To find a 90% confidence interval for the difference in mean numbers of police emergency calls per shift between the two districts, we use the two-sample confidence interval formula for the difference of means:

\[
\left( \bar{X}_1 - \bar{X}_2 \right) \pm Z_{\alpha/2} \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\]

### Given Data:
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Campaign
1	2	3
0.33	0.28	0.21
0.29	0.41	0.30
0.21	0.34	0.26
0.32	0.39	0.33
0.25	0.27	0.31

Student	With Imagery	Without Imagery	Student	With Imagery	Without Imagery
1	20	5	11	17	8
2	24	9	12	20	16
3	20	5	13	20	10
4	18	9	14	16	12
5	22	6	15	24	7
6	19	11	16	22	9
7	20	8	17	25	21
8	19	11	18	21	14
9	17	7	19	19	12
10	21	9	20	23	12

	Developing Section	Rest of the City
Sample size	50	100
Number favoring proposa	38	65

Worker A	19	22	24	27	24	18	20	19	25
Worker B	26	37	40	35	30	40	26	30	35	45