Search & Filtering
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.
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]
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. What is the appropriate distribution to use? Motivate your answer
3. A certain report claims that less than 40% of BTS fans based on Southeast Asia come from
the Philippines.
H 0 : ___________________________________________________________
H a : ___________________________________________________________
1.Find the domain of the function 𝑓(𝑥)=log4(𝑥2+4𝑥−5𝑒𝑥−1).
2. Construct the tangent line to the graph of the function 𝑓(𝑥)=√𝑥+2𝑥 which is perpendicular to the line 𝑥+3𝑦−2=0.
3. Find the maximal intervals of monotonicity of the function 𝑓(𝑥)=arctg(𝑥2−4𝑥).
4. Calculate the integral ∫𝑥2(𝑥3+4)2 𝑑𝑥2−1.
5. Find the particular solution of the differential equation 𝑦′=−(2𝑦+1)⋅tg(𝑥) which fulfills the initial condition 𝑦(𝜋4)=12.
6. Solve the matrix equation 2𝒳+𝒜=3ℬ−𝒜𝒳 if 𝒜=(−4−332), ℬ=(1−121).
1. Solve the matrix equation 4𝒳−ℬ=𝒳ℬ+2𝒜 if 𝒜=(−2141), ℬ=(71−72).
2. Calculate the inverse matrix to the matrix 𝒜=(001011111). Check whether the obtained inverse matrix is correct.
3. Solve the system of linear equations: 𝑥−2𝑦+𝑧=5,−2𝑥+3𝑦−𝑧=−8,−𝑥−𝑦+2𝑧=2.
4. Calculate the area of the flat shape bounded by the curves: 𝑦=√𝑥−1,𝑦=3−𝑥,𝑦=0.
5. Find all the extrema of the function 𝑓(𝑥)=√16−𝑥2.
6. Find the maximal intervals of convexity (concavity) of the function 𝑓(𝑥)=2𝑥+arctg(3𝑥). Find the respective inflection points.
Find each of the following percentile points
under the normal curve.
1. P76
2. P85
3. P39
4. P51
5. P88
A nationwide survey of college seniors by the
University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in
Parade. If 12 seniors are selected at random and asked
their opinion, find the probability that the number who
disapprove of smoking pot daily is
(a) anywhere from 7 to 9;
(b) at most 5;
(c) not less than 8
Adequate knowledge of the content, coupled with the knowledge of the learners,
enables the teacher to plan and modify his/her teaching. Do you agree with
statement? Motivate.
A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population
