Statistics and Probability Answers

A. Find the sample size for each of the following:

a. With 90% confidence, E = 0.08 and p = 0.38.

b. With 95% confidence, E = 0.05 and p = 0.38.

c. With 95% confidence, E = 0.12 and p = 0.38.

d. With 99% confidence, E = 0.20 and p = 0.38.

e. With 99% confidence, E = 0.25 and p = 0.38.

1.What is the advantage of the sample size formula?

2.What is the effect of the level of confidence on the confidence interval?

3.A particular brand of coffee contains an average of 112 mg of caffeine per cup with a standard deviation of 20 mg. Joshua wants to investigate the same to estimate the true population mean caffeine content correct to within 5 mg adopting 95% confidence. How many cups of the same brand of coffee does he need for a sample?

1.    It is claimed that the average weight of babies at birth is 3.4kg. The average weight of a random sample of 30 newly born babies was determined. It was found out that the average weight was 3.1kg. Is there a reason to believe that the average weight of babies at birth is not 3.4kg? Assume that the population standard deviation is 1.1kg. Use 0.05 level of significance.

The probability of a correct answer to a multiple choice question with 4 options

 In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie below 38

Ten android tablets will be delivered to a certain school for testing but three of them are defective tablet, Y represent the nondefective tablet and L represent the random variable representing the defective tablet will occur. Complete the table below and find the values of random variable L.

A population consists of values (2, 3, 5). Consider all possible samples of size n=3 that can be drawn with

replacement from this population.

a. Find the mean of the population

b. Find the standard deviation of the population.

c. Find the mean of the sampling distribution of means.

d. Find the standard deviation of the sample distribution of means.

e. Construct the probability histogram of 𝑥̅ with replacement.

1.Who knows the game sipa? A Physical Education major sought to determine whether all Filipinos are familiar with this game. Among 1,500 respondents, 358 knew the game. Use 95% confidence to estimate the population proportion p and q. Interpret the sample data.

A. Find (^z_a/2)² given each of the following:

^-----------

E

a. With 90% confidence, E = 0.01.

b. With 90% confidence, E = 0.02.

c. With 95% confidence, E = 0.15.

d. With 95% confidence, E = 0.08

e. With 99% confidence, E = 0.05.

1.Estimate the interval for the population proportion from each of the following. Then, interpret the results.

a. X = 500 and n = 1 200 with 95% confidence

b. X =842 and n = 1 200 with 95% confidence

c. X = 610 and n = 1 050 with 95% confidence

d. X = 523 and n = 972 with 99% confidence

e. X = 415 and n = 1 678 with 99% confidence

2.In a survey, 1,000 Grade 7 students were asked if they read storybooks. There were 318 who said "yes." What proportion of the students does not read storybooks? Use 95% confidence interval to determine the population proportion p of all Grade 7 students who read storybooks. Does the data set suggest a positive attitude toward reading?

3.A nutritionist wants to know the population proportion of Grade 1 learners who eat vegetables. pegged at a confidence of a 95%, a survey among 1,200 respondents was conducted and 200 said that they eat vegetables. Interpret the idea.

1.Describe the sampling distribution of proportions.

2.What do you understand by the expression "p is an unbiased estimator of p"?

3.What is meant by the phrase "95% confidence interval for the population p"?

4.A consumer watch group interviewed a random sample of 1,000 consumers and asked them if they are optimistic about the economy or not. There were 612 who said yes. Use 95% confidence level to estimate the population proportions.

1.Compute the population proportion interval estimate given n, p, and the confidence level.

a. n = 300 and p = 0.40 with 95% confidence

b. n = 500 and p = 0.23 with 95% confidence

c. n = 420 and p = 0.61 with 90% confidence

d. n = 670 and p = 0.54 with 99% confidence

e. n = 710 and p = 0.63 with 99% confidence

2.Ismail conducted a poll survey in which 320 and 600 randomly selected voters indicated their preference for a certain candidate. Using 95% confidence level, what is the interval containing the true population proportion p of voters who prefer the candidate?

3.A random sample of 180 users of a new kind of organic shampoo yielded p = 0.64. Use a = 0.05.

a. What is the point estimate of p?

b. What is the interval estimate of p?

4.A random sample of 156 packets of cupcakes yield p = 0.76. Construct a 90% confidence interval for p.