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The Graduate Record Exam (GRE) is a standardized test required to be admitted to many
graduate schools. A high score in the GRE makes admission more likely. According to the
Educational Testing Service, the mean score for takers of GRE who do not have training
courses is 555 with a standard deviation of 139. Brainpower Philippines (BP) offers expensive
GRE training courses, claiming their graduates score better than those who have not taken any
training courses. To test the company’s claim, you as a statistician randomly selected 30
graduates of BP and asked their GRE scores. The random sample of 30 graduates he obtains
recorded a mean score of 560 in GRE. (Level of Significance α = 0.05)
Identify the test statistic to be used and the following;
1. x̅= ___
2. s or σ = ___
3. H0: ___
4. H1: ___
5. μ = ___
6. α = ___
7. ZC or tC = ___
8. Zα or tα = ___
9. Decision rule: ___
10. Draw the rejection region: ____
11. Decision: ___
12. Conclusion:
Consider the real space R3
The following vectors form a basis S of R3:
u1 = (1, −1, 0), u2 = (1, 1, 0), u3 = (0, 1, 1)
Find the coordinate vector [v] of v = (5, 3, 4) relative to the basis S .
A researcher is testing the hypothesis that all teenagers spend an average of 8 hours on their computers during the weekends. He knows that the standard deviation is 0.3 hour. He selects a sample of 144 teenagers and decides to reject the null hypothesis when the sample mean is 8.5 hours or less.
A. What us the probability of that the researcher commits a type I error?
B. If the true population mean is 7 hours, what is the probability that the he commits a type II error?
C. Determine the power of test.
Let
L(x,y
) be the statement “xl loves y,” where the universe of discourse for both x and y consist of all people in the world. Express each of these quantifications in English. (a)
Every body loves somebody.
(b)
There is somebody whom everybody loves.
(c) There is somebody whom Lynn does not love.
A mathematics teacher in senior high school developed a problem-solving test to randomly selected 40 grade 11 students. These students had an average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.
A ball is drawn from a box containing 6 red balls, 4 white balls and 5 black balls . What is the probability that it is not red ball?
Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.
a. Describe the sampling distribution of the sample means
b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.
Two groups of Unam students went into the shop. The first group bought five hamburgers and seven cool drinks and paid N$ 143.50. The second group bought six hamburgers and eight cool drinks and paid N$ 168.50. Deduce the prices for these items (hamburgers & cool drinks)?
Women weight are on average 65kg with a standard deviation of 5kg.Mens weight are on average 75kg with a standard deviation of 10kg.Estimate the percentage of the population whose weight are more than 55kg assuming the number of men and women are equal.
An insurance company found that 45% of all insurance policies are terminated before their maturity
date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a
Binomial experiment.
Required:
a) What is the probability that eight policies are terminated before maturity?
b) What is the probability that at least eight policies are terminated before maturity?
c) What is the probability that at most eight policies are not terminated before maturity?
#340153 on Dec 2023