Reference no: EM132174699

Question One

The members of parliament of People's Republic of Dabanga, a developing country claim that their work is being frustrated by the central Government's failure to facilitate them especially in the area of transport. The parliamentary Commission thinks they travel for 30 minutes daily from their constituencies to the parliamentary building. However members of parliament think they travel for at least 35 minutes. The Commission has tasked with the assignment of finding out what is happening and you decide to carry out a survey whose results are as per below are the raw facts indicating time taken by each of the 210 members of Parliament in minutes.

2	12	23	81	63	51	41	42	71	43	74	49	21	46
11	6	13	24	52	28	47	29	22	21	56	48	43	34
22	21	14	3	25	29	27	31	23	22	53	25	33	45
21	28	5	15	16	26	32	25	51	2	22	21	54	35
54	82	32	17	9	27	7	59	26	29	21	21	38	22
76	25	53	24	16	4	18	28	76	29	13	9	55	27
23	35	24	21	75	17	28	19	9	11	13	19	18	6
45	28	44	27	31	18	19	8	12	12	13	14	7	17
55	26	46	58	27	23	37	11	11	21	22	23	15	16
34	79	33	28	23	43	91	36	29	29	77	51	26	36
42	36	24	32	46	26	21	98	25	39	28	25	45	21
22	34	57	33	21	34	33	56	34	28	21	22	52	23
32	37	41	35	42	31	26	36	34	29	44	39	21	25
41	31	34	47	34	33	48	36	34	37	43	37	44	50
38	38	41	34	47	39	35	48	32	39	38	49	35	60

Working closely with the Head of administration of the parliamentary commission who also doubles as the Human resources Manager, you have decided to compress the above data in form of a frequency distribution based on the following classes

Classes
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99

Required

1. Construct a frequency distribution table showing the time in minutes taken by the parliamentary members using the above classes.

2. Using the data above obtain and explain the following

1. The Mean travel time
2. The median Travel time
3. The Modal Travel time for the Members of Parliament

3. The negotiations for transport facilitation are under way and the above measures are being debated. The Executive is insisting on using the modal time while the Parliamentarians are insisting on using the mean as the measure of central tendency. Justify the choice by each category

4. Calculate and explain the meaning of: Why would one prefer the use of Standard Deviation to the range as a measure of dispersion?

5. Test the hypothesis that the mean time taken to travel by an MP is at least 35minutes against an alternative it is less at 5% level of significance and make a conclusion. What advice would you offer to the Commission?