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Question 1

(a) Determine whether the following statements are TRUE or FALSE.

(i) The trial in binomial distribution is dependent.
(ii) In a Poisson distribution, events must occur independently of each other.
(iii) The Poisson distribution is a continuous probability distribution.
(iv) The area under the graph of a uniform distribution is always greater than 1.
(v) The mean and standard deviation of the exponential distribution are equal.
(vi) The exponential distribution is symmetric. ^QulmGjcU

False True True False True False ^N6E0ME4v

(b) You want to test if the average blood pressure of a man differs from 120 mmHg. You collects a random sample of 12 men and record their blood pressure. You want to do the t-test in R as follows:

```r
library(BSDA)

bp_data <- c(122, 121, 119, 118, 125, 124, 126, 130,
             122, 121, 119, 125)

t.test(Bp_Data, mu=120, sigma=15, alternative =
"greater than")
```

List three errors in the code. ^cccCRsEm

T-test does not have a sigma parameter ^bDiPRM6d

t.test only accepts alternative = {"greater“, ”less“, "two.sided"} ^sIjgZaUg

bp_data. R is case-sensitive ^G4VO9YVO

(c) Provide a different 3x3 matrices for

(i) lower triangular matrix,
(ii) identity matrix, and
(iii) diagonal matrix. ^QnEWwFox

Question 2

(a) Fill in the blanks with the correct answers.

(i) The SAMPLING DISTRIBUTION is used to estimate the population mean.
(ii) The AVERAGE of the mean is the distribution of all possible sample means if you select all SAMPLES of a given size.

(b) Greenbull company claims that its new energy drink increases the average attention span of students. The average attention span without the drink is 42 minutes. Mr. Joe, a researcher in that company conducts an experiment on a random sample of 25 students. He finds that the sample mean and standard deviation of attention span is 44.5 minutes and 5 minutes, respectively. At 5% significance level, he wants to test whether the energy drink has significant effect on attention span.

(i) What are Mr. Joe's hypotheses for this research?
(ii) What kind of test statistic that he should use? Justify your answer.

(c) Give two examples of the following sampling methods

(i) probability
(ii) non-probability

^LW5xbQsa

(I) Mr. Joe's hypothesis for this research is that the average attention span of a student with the drink is greater or equal to 44.5 minutes

H_O : Attention span with the drink is less than 44.5 minutes H_1 : Attention span with the drink is greater or equal to 44.5 minutes

(ii) The test statistic that he should use is t-test because this does not meet the requirements of z-test, the central limit theorem, where n >= 30.

(c) (i) ^plRrJmAw

Element Links

EQjbxyUv: UAS 24-25 FAD1015 Mathematics III

NKJv7MTT: UAS 24-25 Answering Guide#Question 2 — Sampling Distribution, Hypothesis Test, Sampling Methods

7Nu8hFBe: FAD1015 L20 — Sampling Distribution of the Mean#1.2 Types of Samples

OE5ohr76: UAS 24-25 FAD1015 Mathematics III#Question 3

LtVTLegb: UAS 23-24 FAD1015 Mathematics III#Question 4

koTOpmMc: UAS 24-25 FAD1015 Mathematics III#Question 5

TO3aHUBJ: UAS 24-25 FAD1015 Mathematics III#Question 6

%%

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