Statistics and Probability Answers

The fasting blood sugar (FBS) of 15 randomly selected patients is given below:

110, 118, 130, 140, 142, 146, 112. 100, 95, 98, 96, 122, 123, 124, 130

 Do you think that the mean FBS of the patients in the population is 110? It is known that the population variance of FBS is 300.

The daily duration of telephone calls received by the enquiry department of a small industry for a randomly selected 11 days over a quarter is as follows:

160, 172, 121, 144, 100, 108, 175, 200, 105, 95, 102 

The manager of industry says that the population variance of the daily duration of calls over the quarter is 1500. The authority thinks that it is over estimated. Justify the claims of the manager at 5% level of significance.

13.      A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. One percent of the population actually has the disease. Calculate the probability that a person has the disease given that the test indicates the presence of the disease.

  11.   (a)       State and prove Bayes’ theorem.

(b)       In a bolt manufacturing factory, machines and  produce 25%, 30% and 45% of the total outputs, respectively. Of their outputs, 7%, 6% and 4% are defective bolt, respectively.

(i)                What is the probability that a bolt drawn at random from production will be defective?

(ii)             If a bolt drawn at random from production is found to be defective, what is the probability that it was manufactured by machine ?

  5.    Suppose that  

i. For what values of  are  and  mutually exclusive? For this value of , are

                          A and B independent?

           ii. For what values of , are  and  independent?

           Determine whether for this value of x, A and B are mutually exclusive.

A farmer wants to test whether the average yield for three farms is the same, samples of yields over a period of five years were taken from each of the farms the computations have been made

Between sum squares 70

Within sum of squares 122

1)find the null and alternative hypothesis

2) compute the value of f and determine whether is a difference in the yields of the three farms