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It is known that cellular phones batteries by a certain factory have lifetimes that follow a normal distribution. The average lifetime of the batteries is known to be 2.4 years. A random sample size of 16 will be taken.
1. Determine the mean and the standard error of the sampling distribution of the means.
2. What is the distribution of the sampling distribution of the sample mean?
3. What is the probability that a random sample size of 16 will have a sample mean greater than 2.5 years?
4. What is the probability that a random sample of size 16 will have a sample mean of less than 2.2 years?
Given the population: 1, 3, 4, 6, and 8; and suppose samples of size 3 are drawn from this population:
1. What is the mean and standard deviation of the population?
2. How many different samples of size n=3 can be drawn from the population? List them with their corresponding means
3. Construct the sampling distribution of the sample means.
4. What is the mean of the sampling distribution of the sample means?
5. What is the standard deviation of the sampling distribution of the sample means?
Given population 15, 12, 6, 9, and 17. Suppose samples of size 3 are drawn from this population. Complete the table and draw the sketch of histogram. Describe the distribution
In particularly community,it is claimed that the mean household water usage for a particular month is 48 cubic meters. The following year,a country wide water conservation campaign was conducted.Forty five homes were randomly selected and found that the mean comsumption is 52 cubic meters with a standard deviation of 4 cubic meters.Is there enough evidence to say that the mean household water usage per month is higher than 48 cubic meters at a=0.01?
An academic organization claimed that Grade 11 students study time is at most 200 minutes per day, on average. Another survey was conducted to find whether the claim is true. The group took a random sample of 30 students and found a mean study time of 240 minutes with standard deviation of 100 minutes.
Answer the following:
Parameter:
Claim:
Claim ( in symbol ):
Ho: Ho:
Ha: Ha:
What is the significance level or a?
Is it two-tailed or one-tailed test?
2. A researcher claims that the average salary of a private school teacher is greater than P20,000 with a standard deviation of P5,000. A sample of 20 teachers has a mean salary of P25,000. Test the claim of the researcher. At 0.05 level of significance, test the claim of the researcher.
Answer the following:
Parameter:
Claim:
Claim ( in symbol ):
Ho: Ho:
Ha: Ha:
What is the significance level or a?
Is it two-tailed or one-tailed test?
Create at least three real-life situations that show TYPE 1 and TYPE 2 errors.
1.
2.
3.
Tell whether the following conclusions/situations shows TYPE 1 ERROR, TYPE 2 ERROR, or CORRECT DECISION.
1. Jaden finds out that his null hypothesis is true and he fails to reject it.
2. Mia finds out that her null hypothesis is true and she rejects it.
3. Zayn finds out that his null hypothesis is false and he fails to reject it.
4. Camila finds out that her null hypothesis is false and she rejects it.
5. A resort owner closes the pool when it needs to be closed.
6. A resort owner does not close the pool when it needs to be closed.
7. A resort owner closes the pool when it does not need to be closed.
8. A quality control expert does not conclude that the solar panel is effective when it is actually effective.
9. We concluded that P20,000 is the basic salary of the private school teachers when it is not really P20,000.
10. A businessman chooses to establish a milk tea shop in an area where demand is high enough.
Test the hypothesis. Show the step-by-step process in testing hypothesis.
1. A researcher claims that the average salary of a private school teacher is greater than P35,000 with a standard deviation of P7,000. A sample of 35 teachers has a mean salary of P37,000. Test the claim of the researcher. At 0.05 level of significance, test the claim of the researcher.
2. A researcher reports that the average salary of a college dean is more than P65,000. A sample of 35 college deans has a mean salary of P67,000. At 0.01 level of significance, test the claim that the college deans earn more than P65,000 a month. The standard deviation of the population is P5,250.
1. A study shows that the average daily coffee consumption of a 20-30 years old students is 3 cups per day. A university claims that their students tend to drink less than 3 cups. They selected 20 students and found the mean of 3.5 with a standard deviation of 1.5 cups. Use 0.01 level of significance to test their claim.
Answer the following:
Parameter:
Claim:
Claim ( in symbol ):
Ho: Ho:
Ha: Ha:
What is the significance level or a?
Is it two-tailed or one-tailed test?
