Math Answers

Compute the z-statistic for each given claim (p), the observed proportion (p^), and the given

sample size (𝑛).

𝑝 = 0.66, p^= 0.61, 𝑛 = 40

Compute the z-statistic for each given claim (p), the observed proportion (^p), and the given

sample size (𝑛).

𝑝 = 0.2, ^p= 0.18, 𝑛 = 50

Find an expression for a square matrix A satisfying A squared

= In, where In is the n × n identity matrix. Give 3

examples for the case n = 3. 

Inregrate "\\int \\frac{\\cos x dx}{\\sin^2 x}"

suppose that A,B,C and D are matrices with the following sizes: A(5 x 2) B(4 x 2) C(4 x 5) D(4 x 5)

determine in each of the following case whether a product is defined. if it is so then give the size of the resulting matrix.

i) BD

ii) AC - B

iii) DC + A

A taxi driver claims that his average monthly income is Php 2, 800.00 with a standard deviation of Php 250.00 . A sample of 25 drivers were surveyed and found that their average monthly income is Php 3,500.00with a standard deviation of Php 350.00.Test the hypothesis at 1% level of significance.

A. Solve the problems by following the steps and procedures in hypothesis testing. (20 points)

1. A school teacher suspects the claim that the mean number of students that use library 

materials in a certain school is at most 450. To check the claim, the professor checks a 

random sample of 100 library records and obtain that the mean number of students 

using library materials is 458 with a standard deviation of 9. What would the teacher's 

conclusion use 0.05 level of significance? (10 points)

2. prospective MBA student was made to estimate the difference in the salaries of 

professors in private and state universities. An independent study of simple random 

samples of the most recent MBA graduates of both universities revealed the following 

statistics: Conduct a test using 0.01 level of significance. (10 points)

Salary x¯ s n

Private 52,285/mo. 2,400 49

State 50,188/mo. 2,100 49