Statistics and Probability Answers

XY company claims that their lightbulb can last for 6,000 hours. 24 samples were tested, and the average lifespan is 5600 hours with a standard deviation of 300. is there a convincing evidence that the XY lightbulbs cannot last for 6,000 hours?

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) calculate the test statistic value

Determine the appropriate test statistic to be used in the given statements. And then, make an inference by following the steps in testing hypotheses.

Coca-Cola produced 1.5 liters of soda. The production department reported that the standard deviation of the bottle is 0.7 liter. The quality control department conducted a random checking on the content of the bottles and obtained 1.45 liters from 100,1.5 liters bottles. Test if there's enough evidence that the average amount in bottles is different from the standard 1.5 liters. Use a 5% level of significance.

A researcher is conducting a study on the average time consumed by HS students in playing mobile games. A sample of 50 HS students has an average of 200 minutes. Test the null hypothesis that the average time consumed by students is 240 minutes with a population standard deviation of 20.

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) calculate the test statistic value

A teacher claims that the average of students enrolled in Statistics is 88. A sample of 25 Statistics students has an average of 86 and standard deviation of 4. Is there enough evidence to reject the teacher's claim?

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) Calculate the test statistic value

Consider the following information P(A)=0.25 P(Bc)=0.40 and P(A and B)=0.08,Then P(A|B)is 0.2

A population consists of 1, 5, 6, 8, 12, 7, and 11. Suppose a sample of size 3. Find the 

mean and variance.

2. The scores of individual students on a national test have a normal distribution with mean of 18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, solve for the following:

a. determine the mean and standard deviation of the sampling distribution of the sample mean.

b. find the probability that the sample mean falls between 17 and 20 (𝑃(17 < 𝑥̅< 20).

c. the number of sample means that is above 19.3 kilograms.

1. A population consists of six values (6, 9, 12, 15, 18, and 21).

a. Select a random sample of size 3. Explain the random sampling that you used.

b. How many possible samples can be drawn?

c. List all possible samples and compute the mean of each sample.

d. Construct a frequency distribution of the sample means obtained in step 2 including 𝑥̅; 𝑓; 𝑃(𝑥̅); ̅𝑥 ⋅ 𝑃(𝑥̅); ̅𝑥 2 ⋅ 𝑃(𝑥̅); Σ𝑃(𝑥̅); Σ𝑥̅⋅ 𝑃(𝑥̅) 𝑎𝑛𝑑 Σ𝑥̅ 2 ⋅ 𝑃(𝑥̅).

2.) Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100.

a. What is the minimum score necessary to be in the top 15% of the SAT distribution?

b. Find the range of scores that defines the middle 80% of the distribution of SAT scores.

3. )The government would like to conduct a subsidy program for the lowest 5 percent of the families in terms of income. The government gathered data about family income and it’s found to be normally distributed with a mean of Php 130 000 and a standard deviation of Php 50 000. What is the cutoff income for the government program?

1.) In a National Achievement Test, the mean was found to be 75 and the standard deviation was 15. The scores also approximate the normal distribution.

a. What is the minimum score that belongs to the upper 15% of the group?

b. What is the two extreme scores outside of which 15% of the group are expected to fall?

c. What is the score that divide the distribution into two such that 75% of the cases below it?

d. Estimate the range of scores that will include the middle 45% of the distribution.