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Sta2260:Statistics Question Paper
Sta2260:Statistics
Course:Bachelor Of Horticulture
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) Define the following terms as used in statistics i. Statistics ii. Sample iii. Raw data. (6 Marks) b) The following were the marks out of 20 obtained in a statistical exam. Class Frequency 0-4 14 5-9 1 10-14 3 15-19 9 20-24 16 25-29 11 30-34 14 35-39 5 40-44 4 45-49 1 Using the above data, calculate; i. The Arithmetic mean. (3 Marks) ii. Variance (5 Marks) iii. Standard deviation (1 Mark) c) A life Insurance salesman sells on the average 3 insurance policies per week use the Poisson law to calculate the probability that in a given week he will sell i. Some policies (3 Marks) ii. 2 or more policies but less than 5 pieces. (4 Marks)
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d) An experiment was carried out in which it was found that the length of 10 particular species of animals were as follows; 12.3, 11.8, 11.6, 12.6, 13.4, 12.8, 11.1, 12.1, 14.8 and 13.1 respectively. Given that the heights are approximately normally distributed with variance 1.44cm. Construct a 95% confidence interval for the mean of the population of the animal species. (8 Marks)
QUESTION TWO (20 MARKS)
a) Define the following terms; (6 Marks) i. Statistical hypothesis ii. A null hypothesis iii. Level of significance b) In an experiment in which the marks awarded formed approximately a normal distribution there were 10 candidates from each of the three schools. The marks obtained were as follows; School A: 51 24 45 30 13 64 15 9 21 91 School B: 94 43 80 22 99 29 84 76 97 60 School C: 65 49 60 06 67 02 55 18 49 32 Carry out an ANOVA and examine the hypothesis that there is no essential difference between the schools. ?= 0.05 (14 Marks)
QUESTION THREE (20 MARKS)
a) A die is tossed 3 times use binomial distribution to determine the probability of no 5 curning up. (4 Marks) b) State any two advantages and two disadvantages of arithmetic mean. (4 Marks) c) 3000 observations were made from a random variable and a theoretical “expected” distribution was calculated using the total frequency to obtain the following table for comparison. ??1 ??2 ??3 ??4 ??5 ??6 ?? 620 530 490 410 370 580 E 500 500 500 500 500 500 Comment on the fit using a ??2 test. ?= 0.05 (12 Marks)
QUESTION FOUR (20 MARKS)
a) State three (3) ax ioms of probability. (3 Marks) b) Suppose that we want to determine on the basis of the following data whether there is a relationship between the time in minutes it takes a secretary to complete a certain form in the morning and in the afternoon.
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Morning (x) Afternoon(y) 8.2 8.7 9.6 9.6 7.0 6.9 9.4 8.5 10.4 11.3 7.1 7.6 9.0 9.2 6.6 6.3 8.4 8.4 10.5 12.3 Compute and interpret the sample correlation coefficient. (12 Marks) c) The average on a statistical test was 78 with a standard deviation of 8. If the test scores are normally distributed. Find the probability that a student receives a test score greater than 85. (5 Marks)
QUESTION FIVE (20 MARKS)
The following data pertains to the chlorine residuals in swimming pool at variance times after it has been treated with chemicals.
No. of hours Chlorine residual (parts/millions) 2 1.8 4 1.5 6 1.4 8 1.1 10 1.1 12 0.9 i. Find a least square line from which we can predict the chlorine residuals of the number of hours since the pool was treated with chemicals. (10 Marks) ii. Usethe equation of the least square line to estimate the chlorine residuals in the pool 5 hours after it has been treated with chemicals. (10 Marks)
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