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Question 1: Marks: 7 + 3 = 10
a) A General Incorporated Mill’s packing machinery is known to pour dry cereal into economy size boxes with a standard deviation of 0.6 ounce. The two samples, taken from two machines, yield the following information:

Machine A Machine B

n1=21 n2=15
X1=21.9 X2=18.7





Assume the Machine-A is N(u1,0.36) and Machine-B is N(u2,0.36) , construct the 95.44% confidence interval estimate for .

b) Why we call the standard deviation of sampling distribution of a statistic as the standard error of the statistic?

Question 2: Marks: 10
A random sample of 100 recorded deaths in an urban city during the past year showed an average life span of 71.8 years, with a standard deviation of 8.9 years. Does this seem to indicate that the average life span today is greater than the 70 years? (Use a 0.05 level of significance.)


Question 3: Marks: 10
A population consist of N = 4 numbers 1, 3, 4 and 5. Find the proportion of odd numbers in ALL possible samples of size n = 3 drawn without replacement by using the rule of combination.
Also construct the sampling distribution of the proportion of odd numbers and find mean and variance of the sampling distribution.