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A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.
Which is the correct null hypothesis that can be derived in the situation?
Which is the correct alternative hypothesis that can be derived in the situation?
What test will be used based from the given values in the situation?
What is the decision based from the critical value and the computed test statistic?
Jam, a cat lover, has five pet cats at home. She feeds them
organic cat food because she claims that feeding the cats
with cat food had an impact on the cats’ lifespan. According
to a study, the mean lifespan of cats is 12 years.
- State the null hypothesis (in words and symbols)
- State the alternative hypothesis (in words and symbols)
- Is the test one-tailed or two-tailed? Explain in 1-2 sentences.
- Explain whether the decision was correct or not.
For item 4, use the decision below as your reference.
The null hypothesis was not rejected, and it was found out later that feeding cats with
organic food do not impact a cat’s lifespan.
In an advertisement, a certain brand of shampoo is claiming that
the use of this product will make the hair grow faster. It is known
that the mean length of growing hair over thirty days is 2 cm. What would be its H0 and H1?
The federation of private school teachers has developed a
new evaluation instrument that they claim has higher
reliability by producing less error in evaluation. In the past, the
mean number of errors in the evaluation was 20%. What would be its H0 and H1?
There are five card in a box containing the numbers 1,3,5,7 and 9. A sample of size 3 is to be drawn at a time. Construct the sampling distribution of the mean.
a.) How many possible samples can be drawn?
b.) List all the possible samples and the corresponding means.
c.) Construct the sampling distribution of the sample means.
d.) Draw the histogram for the sampling distribution of the sample means.
e.) What is the shape of the histogram of the sampling distribution of the sample means?
ASSIGNMENT F10 (HYPOTHESIS TESTING)
Identify the null and alternative hypothesis of the ff.
1. The average age of bus drivers in a certain city is 38.8 years.
Ho :
Ha :
2.A university claims that the proportion of its students who graduate in four years is more than 82%.
Ho:
Ha :
3.A television manufacturer claims that the standard deviation of life of a certain type of television is 3 years.
Ho :
Ha :
Identify the null and alternative hypothesis of the ff.
4.The average number of calories of a low-calorie meal is at most 300.
Ho :
Ha :
5.The school record claims that the mean score in Math of the incoming grade 11 students is 8.1. The teacher wishes to find out if the claim is true. She tests if there is a significant difference between the batch mean score and the mean score of students in her class.
Ho :
Ha :
You would be introducing a new curricular program in your university to increase the enrolment because the university’s enrolment has been declining for the past years. Initially, you would want to find out whether such academic program will be the preferred course by the incoming students. What technique would you use and why?
The heights of grade 11 male students are normally distributed with a mean of 65 inches and a standard deviation 2.25 inches. (a) Find the values of 45.75 inches and 72.5 inches. (b) What is the probability that a randomly chosen member of the group has height x berween 60 inches and 70 inches?
A researcher wants to determine if review sessions affect the performance of the students in written exams. A review session is administrated to sample of 25 students and after the examination, a sample mean of 43 was calculated with a standards deviation of 8. From the previous examinations, it was identified that the population mean for the same exam is 40. Can the researcher conclude that the review session is effective in improving the students’ exam results? Use a = 0.01.
In a job fair, 3000 applicants applied for a job. Their mean age was found to be 28
with a standard deviation of 4 years.
a.
Draw a normal curve distribution showing the z-scores and the raw scores.
b.
How many applicants are below 20 years old?
C.
How many applicants are above 32 years old?
d. How many have ages between 24 and 32 years?
e.
Find the age such that 75% is below it.
