Search & Filtering
let ′ ∣ ′ be the divides relation on a set of positive integers. That
is ∀𝑎, 𝑏 ∈ 𝐴, 𝑎 ∣ 𝑏 ⇔ 𝑏 = 𝑘. 𝑎 for some integer 𝑘. Prove that ∣ is a partial order
Relation.
Let ‘R’ be a relation defined on a set of integers Z as follows:
∀ 𝑎, 𝑏 ∈ 𝑍, 𝑎𝑅𝑏 iff 𝑏 = a^r
for some integer 𝑟. Show that R is a partially
ordered relation.
Activity 2
Find the rejection region for each hypothesis test based on the information given.
1 H₂ μ = 121
Hah > 121 Η μ=986
2. Ho:μ=986 Ị Hai =27
HaiH <27
a= 0.01
a= 0.05 a= 0.05
n=34
known unknown
n=25 n=12
a known
ASSESSMENT
Perform as indicated
In numbers 1-5, find the critical valuets) and rejection remonts) for the type of z-test with level of significance a Include a graph with your answer
1 Left -tailed test, a=0.03
2 Right-tailed test = 0.05
3 Two-tailed test, a = 0.02
4 Two-tailed test, a = 0.10 5 Left-tailed test, a=0,09
In numbers 6-9, state whether each standardized test statistic z allows you to reject the null hypodesis Explain your reasoning
6. z=-1301 7 z=1203
8 2 1.280 9 2=1.286
10 A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no
more than 920 milligrams A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams Aanume the population standard deviation is 15 milligrams At a=0.10, do you have enough evidence to reject the restaurant's claim?
Activity 3 region
Find the critical value of each given problem. Skatch the curve and shade the wjection
1 14-90
The sample mean is 69 and simple size is 35 The population follows a normal distritsation with standard deviation 5 Usca w 0.05
2. A redaurant cashier claimed that the average amount spent by the endomers for dinner is P125.00 Over a month period, a sample of 50 customers was selected and it was found that the everage amount spent for dinner was P130.00 Using 005 level of significance can it be concluded that the average amount spent by customers is more than P125.00 Astose that the population standard deviation is 7.00
1. Determine an initial basic feasible solution to the following transportation problem by using (a) the least cost method, and (b) Vogel’s approximation method. Based the initial basic feasible solution that is relatively small conduct a modified distribution method to determine the optimum solution to the problem.
Source
Destinations
Supply
D1
D2
D3
D4
S1
1
2
1
4
30
S2
3
3
2
1
50
S3
4
2
5
9
20
Demand
20
40
30
10
JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2
and M3
. Belt A requires 2 hours on machine(M1)
and 3 hours on machine (M2)
and 2 hours on machine (M3). Belt B requires 3 hours onmachine (M1)
, 2 hours on machine (M2)
and 2 hours on machine (M3)
and Belt C requires 5hours on machine (M2)
and 4 hours on machine (M3)
. There are 8 hours of time per dayavailable on machine M1
, 10 hours of time per day available on machine M2
and 15 hoursof time per day available on machine M3
. The profit gained from belt A is birr 3.00 per unit,from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a)
Formulate the problem as LPM
b)
Solve the LPM using simplex algorithm.
c)
Determine the range of feasibility, optimality and insignificance
d)
Interpret the shadow price
A population consists of five numbers 1, 2, 3, 4, 5 and 6. Suppose samples of size 2 are drawn from this population.
(a) Find the mean and variance of the population
(b) Describe the sampling distribution of the sample means.
(c) Find the mean and variance of the sampling distribution of the sample means.
The linear isometry F:l'"\\to" (l^infinity)' given b F(y)=fy, y"\\isin" l' is not surjective
Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance.
i. What is the appropriate distribution to use? Motivate your answer. [3]
ii. State your hypotheses. [2]
iii. Is there a claim? What is the claim and in which part of the hypothesis does the claim resides? [3]
iv. Use a distribution curve to determine the rejection and non-rejection region using critical values for the appropriate distribution. [5]
v. Calculate the test statistic of the distribution. [2]
vi. Compare your test statistic to the critical value. [2]
vii. State both your statistical and a management conclusion. [3]
