Problem 1 the following 10 samples were collected on random

Question

Problem 1: The following 10 samples were collected on random variable U from a large population with replacement. Calculate the statistical estimates below.

U = [1.99, 1.94, 2.03, 2.05, 1.88]

Sample mean of U =

Sample variance of U (unbiased) =

If the true variance of U is 0.0007, what must be the sample size, n, for the unbiased sample variance to be 0.0068?

Problem 2: For an ECE 420 course exam taken by 25 students, the true mean is 75 and the true variance is 10. It is desired to estimate the mean by sampling without replacement.

If 10 scores are used, calculate the standard deviation of the sample mean.

σ (sample mean) =

How large must the sample size be to have a standard deviation of the sample mean be two percentage points out of 100.

N =

How large must the sample size be to have the standard deviation of the sample mean be one percent of the true mean?

Problem 3: You own a manufacturing company that produces analog video amplifiers; however, the voltage gain varies according to a Gaussian distribution. You would like to claim with 99% confidence on the datasheet that the gain is at least 100.

If 25 amplifiers are tested, what range must the sample mean be for you to make the claim? Your quality assurance department measures 50 amplifiers and obtains a sample mean of 99.5. Is the claim true with 99% confidence and why?

Problem 4: One of your suppliers claims that a transistor has a current gain of at least 100. You measure 15 transistors and find that the sample mean is 99.5 and a standard deviation of the sample mean of 2.

For what confidence level would the supplier's claim be valid?

What must the sample mean be for the claim to be valid with a confidence level of 90%?

Answer 1

In order to answer the following statistics problem, implement the principles and theories of statistics and find out the solution for each part. Problem 1: The given 10 samples were collected on arbitrary variable U from a big population with replacement. Compute the statistical approximates below. U = [1.99, 1.94, 2.03, 2.05, 1.88] If true variance of U is 0.0007, determine the sample size, n, for the un-biased sample variance to be 0.0068? Problem 2: For an examination taken by 25 students, the true mean is 75 and the true variance is 10. This is desired to predict the mean by sampling devoid of replacement. a) If 10 scores are utilized, compute the standard deviation of sample mean. b) Illustrate how large should the sample size be to encompass a standard deviation of the sample mean be 2% points out of 100. c) Illustrate how large should the sample size be encompasses the standard deviation of the sample mean be 1% of the true mean?