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The average amount of rainfall during the summer months is 11.52 inches. A researcher in
PAGASA selects a random sample of 10 provinces and finds that the average amount of
rainfalllast year was 7.42 inches with a standard deviation of 1.3 inches. At 0.01 level
significance, can it be concluded that the mean rainfall last year was below 11.52 inches?
Step
1. State the null and alterative hypothesis
concerning the population mean, "\\mu" and the type of test to be used.
2. Specify the level of significance "\\alpha"
3.State the decision rule.
4. Collect the data and perform calculations.
5.Make a statistical decision.
6. State the conclusion.
Suppose a sample of 20 students were given a diagnostic test before studying a particular module and then again after completing the module. We want to find out if, in general, the module leads to improvements in students’ test scores. Use 5% level of significance. (the output range should be at cell G4)
Before Module: 17,18,15,10,9,6,25,8,29,34,19,35,22,20,19,27,17,20,22,21
After Module: 25,29,30,20,10,6,29,20,35,33,28,39,28,19,27,27,19,29,34,38
A random sample of 20 brand X corned beef while 15 samples of brand Y corned beef were taken, and the data of their mean weight in grams were shown below. Is there a significant difference in the mean net weight of the two brands of corned beef? Set the level of significance at 5%. (the output range should be at cell G4)
Brand X 160, 165, 176, 157, 170, 165, 167, 166, 159, 160, 170, 156, 145, 155, 150, 159, 165, 166, 150, 148
Brand Y 145, 168, 165, 144, 166, 155, 178, 155, 149, 156, 150, 155, 156, 147, 150
The amount of time devoted to preparing for a statistics examination by students is a normally distributed random variable with a mean of 17 hours and a standard deviation of 5 hours.
Required:
a) What is the amount of time below which only 15% of all students spend studying?
b) What is the amount of time above which only one third of all students spend studying? c) What is the probability that a student spends between 16 and 20 hours studying?
d) What is the probability that a student spends at least 15 hours studying?
e) What is the probability that a student spends at most 18 hours studying?
Suppose that a mobile telecommunication company’s helpline receives five calls, on average, per minute.
Required:
a) Discuss the difference between the Binomial probability distribution and the Poisson probability distribution.
b) How many calls does the company expect to receive in a period of 30 minutes?
c) What is the probability that the company will receive at most four calls in a period of 4 minutes?
d) What is the probability that the company will receive at least three calls in a period of 5 minutes?
e) What is the probability that the company will receive between six and nine calls in a period of 2 minutes?
Suppose that the latest census indicates that for every 10 young people available to work only 4 are employed. Suppose a random sample of 20 young graduates is selected.
Required:
a) What is the probability that they are all employed?
b) What is the probability that none of them are employed?
c) What is the probability that at least four are employed?
d) What is the probability that at most fifteen are employed?
e) What is the probability that the number of young graduates who are employed is greater than ten but less than fifteen?
f) What is the expected number of graduates who are not employed?
g) What is the standard deviation for the number of graduates who are not employed?
1.2 Explain how and who came up with these algebraic concepts or used these algebraic concepts developed over time:
1.2.1 Decimal Number System
1.2 2 Abstract Symbols
1.2.3 Negative Numbers
In a survey conducted among a random sample of students the following observations were made regarding their gender and learning environment preferences during the COVID-19 pandemic:
168 prefer online learning
202 prefer face to face learning
180 prefer blended learning
34 male students prefer online learning and
70 male students prefer blended learning
106 female students prefer face to face learning
Required:
a) What is the probability that a female student is chosen?
b) What is the probability that a male student prefers face to face learning?
c) What is the probability that a student prefers online or blended learning?
d) If it’s known that the student is female, what is the probability that this student prefers online learning.
e) Using a practical example, explain the difference between mutually exclusive events and independent events.
suppose f(z) =1/z. write f in the form f(z) = u(x,y) + iv(x,y), where z = x+iy and u and v are real-valued functions
Two balls are drawn in succession without replacement from a box containing 9 black balls (B) and 7 white balls (W). Let Z be the random variable representing the number of white balls. Possible Outcomes Value of the Random Variable Z Number of White Balls (Z) Probab
#340153 on Dec 2023