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ACTIVITY 7. EXPLORING MORE ELEMENTS OF HYPOTHESIS TESTING
A. Complete the table showing the rejection regions for common values of 𝜶.
Alternative Hypothesis
𝜶 Left-Tailed Right-Tailed Two-Tailed 𝛼 = .10 1. ___________ z > 1.28 z < -1.645 or z > 1.645
𝛼 = .05 z < -1.645 2. _________ z < -1.96 or z > 1.96
𝛼 = 0.25 3. ___________ z > 1.96 4. _______________
𝛼 = .01 z < -2.33 5.__________ z < -2.58 or z > 2.58
(b) On the average a certain computer part lasts ten years.The length of time the computer part lasts is exponentially distributed.
i.What is the probability that a computer part lasts between nine and `11` years?
ii.How long does eighty percent of computer parts last at most?
iii.On the average how long would five computer parts last if they are used one after another?
B. State the null hypothesis and the alternative hypothesis in (a) words and in (b) symbols for each of the following:
1. The average age of Youtube users is 25.
(a) In words = Ho: __________ Ha: __________
(b) In symbols = Ho: __________ Ha: __________
2. The mean age of the grade 10 students enrolled in Marawi High School is 16 years old. (a) In words = Ho: __________ Ha: __________
(b) In symbols = Ho: __________ Ha: __________
3. A doctor wants to know if the average recovery time of a patient taking a particular medication is one month.
In words,
Ho: The average recovery time of a patient taking a particular medication is one month.
In symbols,
Ho: ____________
In words,
Ha: The average recovery time of a patient taking a particular medication is not one month.
In symbols,
Ha: μ ≠ 1 month
2. A power company wants to see if the average amount of current passing through a series of connections is larger than 30 milliamperes (mA).
In words,
Ho: _______________________________________________ _______________________________________________
In symbols,
Ho: μ = 30
In words,
Ha: The average amount of current passing through a series of connections is larger than 30 milliamperes (mA).
In symbols,
Ha: ____________
One-tailed or directional test (specifically right-tailed)
ACTIVITY 6. INTRODUCTION TO HYPOTHESIS TESTING
A. Complete the tables by providing the necessary information.
1. The mean grade of a GAS student in a Statistics class is not 80.
In words,
Ho: The mean grade of a GAS student in a Statistics class is 80. In symbols,
Ho: ____________
In words,
Ha: _______________________________________________ _______________________________________________
In symbols, Ha: μ ≠ 80
Two-tailed or Non-directional test
A sample of 20 observations is selected from normal population distribution with
population standard deviation 9 and sample mean 51. Determine the highest
value of population mean with 95% confidence interval (z-1.96). Round the
answer to the two decimal places.
Determine the standard error if a population standard deviation is 31 and sample
size is 19. Round the answer to the two decimal place.
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.
the IQ of 600 police applicants are normally distributed with a mean of 115 and standard deviation of 12. If the police academy requires at least IQ of 95, how many will be admitted?
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