Statistics and Probability Answers

Professor Balenciaga has reported her students' grades for several semesters and the average for all the grades ofthese studs is 83. Her new class of 30 studs seem to be higher than the average of ability and she wants to demonstrate that the current class is superior to the previous classes according to their average. Is ther sufficient evidence for the class average of 86.2 and the standard deviation of 12 present to support her argument that the current class is superior? Using the 0.05 significance level.

Sixteen oil tins are taken at random from an automatic filling machine. The mean weight of the tins is 14.2 kg, with a standard deviation of 0.40 kg. Can we conclude that the filling machine is wasting oil by filling more than the intended weight of 14 kg, at a significance level of 5%? (5 marks)

 The following data relate to advertising expenditure in. Sh. ten thousands and their corresponding sales (in Shs. millions). Advertising expenditure 10 12 15 23 20 Sales 14 17 23 25 21 i.) Fit a regression line of sales against advertising expenditure? (5mrks) ii) Estimate the sales when the advertising expenditure is of sh. 300,000? (2 marks)

Conduct a t-test for the null hypothesis against

alternative hypothesis based on 16 random

observations. The sample mean is 110 and the sample standard

deviation is 10. Use α = 0.05.

8. The average drive to work is 9.6 miles. Assume standard deviation is 1.8. If random sample of 36 employed who derive to work are selected, find the probability that mean of sample miles driven to work is between 9 and 10 miles.

9. The data for the car rental company is given:

Company                    Cars                Revenue

   A                            63                   7

   B                            29                   3.9

   C                            20.8                2.1

   D                           19.1                2.8

   E                            13.4                1.4

   F                             8.5                  1.5

Compute the linear correlation coefficient for the data and find the equation of regression line.

1.      In a hospital unit, there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. In a staff person is selected, find the probability that the subject is nurse or male.

Staff                     females               males                   total

Nurse                        7                          1                         8

Physicians                3                         2                         5

                                  10                          3                        13

null and alternative hypothesis of the problem