Assume we have a box with 10 chips, each with a number written on it from 1-10. Consider this to be our population of scores. What are μ and σ for the population?
Can you please explain how you are doing it and what information you are using for each
Assume we have a box with 10 chips, each with a number written on it from...
A box contains 20 chips. 8 of these chips have a value of $5 and the others have no value. We randomly pick 3 chips from the box and putting them back after each draw. A = Number of chips of $5 after 2 draws. What is the distribution of A?
We have a normally distributed population of scores with μ = 25 and σ = 5. We have drawn a large number of random samples with a particular sample size of n = 10 from this population. We want to know what the probability that a sample mean will be equal to or greater than 23. First, what is the z-score for our sample mean of interest, 23? Using this z-score , use statistics table to answer the question "What...
A box contains seven chips, each of which is numbered (one number on each chip). The number 1 appears on one chip. The number 4 appears on one chip. The number 2 appears on three chips. The number 3 appears on two chips. Two chips are to be randomly sampled from the box without replacement. Let X be the sum of the numbers on the two chips to be sampled. (a) Write out all of the possible outcomes for this...
Consider this testing situation. A box contains 16 chips (with
some mixture of red and black chips). Suppose we have the following
hypotheses:
HO: The box contains R=8 red and
B=8 black chips.
HA: The box contains some other
mixture of red and black chips.
We randomly select 5 chips simultaneously from the box without
replacement. Our Test Statistic is the Y = # of Black chips found
in the sample.
Suppose we use the following decision rule:...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
For a parametric model with distribution N(μ,02), we have: & variance = σ How can we use these formulas to explain why the sample mean is an unbiased and consistent estimator of the population mean?
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white We are going to find MAP estimate...
The Nero Match Company sells matchboxes that are supposed to
have an average of 40 matches per box, with σ = 8. A
random sample of 94 matchboxes shows the average number of matches
per box to be 42.2. Using a 1% level of significance, can you say
that the average number of matches per box is more than 40?
What are we testing in this problem?
single meansingle proportion
(a) What is the level of significance?
State the null...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...