# STA301 Statistics and Probability Final paper 23 February 2013

Q :1 For two independent events A and B with P(A) = 0.6, P(B) = 0.3, find (2 marks)

Q:2 Define standard normal distribution.(2 marks)

Q:3 Formulate the null and alternative hypothesis:
The difference between the average yield of machine A and the average yield of machine B is exactly 40. (2marks)

Q:4Briefly discuss about natural pairing in t-distribution? (2marks)

Q:5 Suppose a person walks on the main street of a large city centre and counts the number of floors in each building as below.
5, 4, 3, 4, 5, 4, 3, 4, 5, 32, 5, 6, 6, 4, 27 (2 marks)
Is arithmetic mean is a suitable measure of central tendency for this data? Explain.
(3marks)
.Q:6If there are k treatments with r blocks in a randomized completed block design. Find the degrees of freedom for treatments, blocks and error. (3marks)
Q:7 Why we prefer to use pooled estimator instead of and? (3marks)
Q:8
If
Then find .(3 marks)

Q:9 In a poll of college students in a large university, a group of 300 out of 400 students living in students’ residences (hostels) approved a certain course of action, whereas another group of 200 out of 300 students not living in students’ residences approved it. Compute the 90% confidence interval for the difference of proportions between both groups, using (5 marks)

Q:10
If is normaly distrbuted with and
then find out the
(3 marks)
Q:11A manufacturer of car batteries claims that the life of his batteries has a standard deviation equal to 0.9 years. If a random sample of 10 of these batteries have a standard deviation of 1.2 years, do you think that <0.9 years? Use a 0.05 level of significance. (5 marks)

Q:12By using an appropriate average find out the average rate of motion in the case of a person who rides the first mile at the rate of 10 miles per hour, the next mile at the rate of 8 miles per hour and the third at the rate of 6 miles per hour.
(5 marks)

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