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STT 620: GRADUATE RESEARCH STATISTICS ASSIGNMENT 3 1. A study conducted finds that a typical office worker spends an average of 13 minutes per hour...

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STT 620: GRADUATE RESEARCH STATISTICS ASSIGNMENT 3 1. A study conducted finds that a typical office worker spends an average of 13 minutes per hour on non work related activities such as face book. On a trial basis, management sets up a new enclosed work station for a randomly selected group of 12 workers and finds that the average number of minutes lost per hour is 11.3 with a standard deviation of 3.7. At the 5% level of significance, can we conclude that the work station represents a significant change? (3 marks) 2. Five hundred graduates were cross classified by socio-economic group and the presence or absence of a certain skill gap. The results were as shown below. Socio- economic group Skill Gap Upper Upper middle Lower middle Lower Present 8 24 32 27 Absent 42 121 138 108 Are the data compatible with the hypothesis that skill gap is unrelated to socio- economic status of the graduates at α = 0.10? (5 marks) 3. The following are the sales revenues (in millions of shillings) generated by four salesmen situated in four different regions of a country. Region A Region B Region C Region D 13 12 18 8 9 11 12 10 12 9 16 12 16 14 6 8 15 4 8 7 Perform a one way analysis of variance at α = 0.05 to confirm whether salesman location influences the amount of revenues generated . (5 marks) 4. The responses from a group of religious leaders on an item of Likert’s attitude scale were recorded as follows: Strongly disagre e disagre e Undecide d Agre e Strongly agree Total
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Christia n 12 18 4 8 12 54 Muslim 48 22 10 8 10 98 Hindu 10 4 12 10 12 48 Total 70 44 26 26 34 200 At 1% level of significance, do the data indicate that the opinions expressed are independent of the religion professed by the respondents? (5 marks) 5. a) The following data were collected from two separate groups of 144 men and 175 women on an attitude scale. Mean SD MEN 19.7 6.08 WOMEN 21.0 4.89 i. Test the significance of the difference between the mean of the two groups at the 0.05 level of significance. ii. In your own words, what does the result of the experiment say? ( 5 marks) b) On the daily run of an express bus, the average number of passengers is 48 with a variance of 9. Assuming that the variable is normally distributed, find the probability that the bus will have: i. Between 36 and 40 passengers ii. Fewer than 42 passengers iii. More than 45 passengers iv. Between 46 and 54 passengers (8 marks)
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