Math Answers

P(z>2.92)

b) two types of engines, A and B, were compared. Gas mileage, in miles per gallon, was measured. 50 experiments were conducted using engine type A and 75 experiments were done with engine type B. The gasoline used and other conditions were held constant. The average gas mileage was 36 miles per gallon for engine A and 42 miles per gallon for engine B. Find a 95% condence interval on "\\mu"_B - "\\mu"_A, where "\\mu"_B and "\\mu"_Aare true mean gas mileages for engines A and B, respectively. population standard deviations are 6 and 8 for engines A and B, respectively. What can you conclude?

a) i) Suppose H₀: "\\mu" = "\\mu" 0 is rejected in favour of H₁ : "\\mu" != "\\mu" 0 at "\\alpha" = 0.05 level of significance. Would H₀ necessarily be rejected at the "\\alpha" = 0.01 level of signicance? Explain.

ii) Suppose H₀: "\\mu" = "\\mu" 0 is rejected in favour of H₁ : "\\mu" != "\\mu" 0 at "\\alpha" = 0.01 level of signficance. Would H₀ necessarily be rejected at the "\\alpha" = 0.05 level of significance? Explain.

iii) If H₀: "\\mu" = "\\mu" 0 is rejected in favour of H₀: "\\mu" > "\\mu" 0, will it necessarily be rejected in favour of H₁ : "\\mu" != "\\mu" 0 ? Assume that "\\alpha" remains the same.

a) Find the appropriate rejection regions for the large-sample z-test in these cases:

i) A right-tailed test with "\\alpha" = 0.01;

ii) A two-tailed test at 5% signicance level;

iii) A left-tailed test with "\\alpha" = 0.05.

b) Find the p-value for the following large-sample z-tests:

i) A right-tailed test with observed z = 1.15;

ii) A two-tailed test with observed z = -2.78;

iii) A left-tailed test with observed z = -1.81.

c) Suppose that an allergist wishes to test the hypothesis that at least

30% of the public is allergic to some cheese products. Explain how the

allergist could commit:

i) a type I error.

ii) a type II error.

d) A large manufacturing firm is being charged with discrimination in its

hiring practices.

i) What hypothesis is being tested if a jury commits type I error by

finding the firm guilty?

ii) What hypothesis is being tested if a jury commits type II error

by finding the firm guilty?

consider the following system of equations:

3x + 4y +5z = 66

7x + 4y +3z = 74

8x + 8y +9z = 136

a. write down the associated augmented matrix for this system of equations and the coefficient matrix A.

b. by performing elementary row operations of the augmented matrix, solve the system of equations or show that no solution exists. In case there exist infinitely many solutions, then the solution to the system must be written in parametric form.

c. Based on your answer in b, what is the rank of the coefficient matrix A?

Design and implement a minimal 5 modulo up counter. It counts from 0 to 4 and repeats.

Design the circuit such that, if the counter enters into the unwanted states: 5, 6 and 7, it should jump into state 0 on the next clock pulse.

v> Dr Mukonda has two cars, which he hires out day by day. The number of

demands follows poisson with mean 1.5. Calculate the probability that on

a day: (a) Neither car is used (b) Some demands is refused.

The range of the sample data is what

Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general?

39

38

36

29

19

18

15

11

10.7

9.9

There is a bag filled with 4 blue and 5 red marbles. 

A marble is taken at random from the bag, the colour is noted and then it is not replaced. 

Another marble is taken at random. 

What is the probability of getting 2 of the same colour?

Find the product of eigen value of matrix