QUESTIONS 1 TO 4 ARE BASED ON THE FOLLOWING INFORMATION. Consider the random variable X with...

QUESTIONS 1 TO 4 ARE BASED ON THE FOLLOWING INFORMATION. Consider the random variable X with a mean 100 and a population standard deviation of 9. Assume a sample of size 30 was used.

Question 1
Consider the statements below.
(A) The 90% confidence interval estimate for the population mean is (97.2970; 102.7030)

(B) The 95% confidence interval estimate for the population mean is (96.7794; 103.2206)

Which statement(s) are correct?
(1) Only A.
(2) Only B.
(3) Only C.
(4) Only A and B.
(5) A, B and C.

Question 2

Assuming the sample size stays the same, what happens to the confidence interval estimate when the level of confidence increases?
(1) The confidence interval estimate doesn’t change.
(2) The confidence interval estimate becomes wider.
(3) The confidence interval estimate becomes narrower.
(4) The confidence interval estimate converges to zero.
(5) None of the above.

Question 3

Which of the following statements is incorrect?

(1) When the sample size is 60 the 95% confidence interval estimate for the population mean is (97.7227; 102.2773)

(2) When the sample size is 100 the 95% confidence interval estimate for the population mean is (98.2360; 101.7640)

(3) When the sample size is 200 the 95% confidence interval estimate for the population mean is (98.7527; 101.2473)

(4) When the sample size is 500 the 95% confidence interval estimate for the population mean is (99.2111; 100.7889)

(5) None of the above.

Question 4

Assuming the level of significance stays the same, what happens to the confidence interval estimate when the sample size increases?

(1) The confidence interval estimate doesn’t change.
(2) The confidence interval estimate becomes wider.
(3) The confidence interval estimate becomes narrower.
(4) The confidence interval estimate converges to zero.
(5) None of the above.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Questions 1-5 are based on the following Let X be a normally distributed random variable. A...

Questions 1-5 are based on the following Let X be a normally distributed random variable. A random sample of size n = 9 yields the following data: x 98 93 61 75 58 75 95 77 70 1 The variance of the sample is, a 210.75 b 201.21 c 191.67 d 187.33 2 The variance of x̅ is, a 62.229 b 74.083 c 23.417 d 34.572 3 You want to build a 95% confidence interval for the population mean. The...

4. Consider the random variable Z from problem 1, and the random variable X from problem...

4. Consider the random variable Z from problem 1, and the random variable X from problem 2. Also let f(X,Z)represent the joint probability distribution of X and Z. f is defined as follows: f(1,-2) = 1/6 f(2,-2) = 2/15 f(3,-2) = 0 f(4,-2) = 0 f(5,-2) = 0 f(6,-2) = 0 f(1,3) = 0 f(2,3) = 1/30 f(3,3) = 1/6 f(4,3) = 0 f(5,3) = 0 f(6,3) = 0 f(1,5) = 0 f(2,5) = 0 f(3,5) = 0 f(4,5) = 1/6...

a. Consider the following distribution of a random variable X X – 1 0 1 2...

a. Consider the following distribution of a random variable X X – 1 0 1 2 P(X) 1/8 2/8 3/8 2/8 Find the mean, variance and standard deviation b. There are 6 Republican, 5 Democrat, and 4 Independent candidates. Find the probability the committee will be made of 3 Republicans, 2 Democrats, and 2 Independent be selected? c. At a large university, the probability that a student takes calculus and is on the dean’s list is 0.042. The probability...

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that...

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that P(X<6)=0.841345 , compute P(2<= x <= 6) 2)Consider X a normal random variable with mean 10 and standard deviation 4. Given that P(x>9)=0.598708 and P(x<12)=0.691464 . Compute P(8< x < 11).

Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show...

Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show steps of your work: a) E[X] b) E[X2] c) Var[X] d) E[(1 – X)10] e) E[(X – p)4] f) E[3x41-x] g) var[3x41-x]

The following 5 questions are based on this information. A random sample of 25 Apple (the...

The following 5 questions are based on this information. A random sample of 25 Apple (the company) customers who call Apple Care Support line had an average (X bar) wait time of 187 seconds with a sample standard deviation (s) of 50 seconds. The goal is to construct a 90% confidence interval for the average (μ) wait time of all Apple customers who call for support. Assume that the random variable, wait time of Apple customers (denoted by X), is...

1. (Memoryless property) [10] Consider a discrete random variable X ∈ N (X ∈ N is...

1. (Memoryless property) [10] Consider a discrete random variable X ∈ N (X ∈ N is a convention to represent that the range of X is N). It is memoryless if Pr{X > n + m|X > m} = Pr{X > n}, ∀m,n ∈{0,1,...}. a) Let X ∼ G(p), 0 < p ≤ 1. Show that X is memoryless. [2] b) Show that if a discrete positive integer-valued random variable X is memoryless, it must be a geometric random variable,...

Consider a discrete random variable with the following probability mass function x 0 1 2 3...

Consider a discrete random variable with the following probability mass function x 0 1 2 3 4 5 p(x) 0.1 0.1 0.2 0.3 0.2 0.1 Generate a random sample of size n =10000 from this distribution. Construct a bar diagram of the observed frequencies versus the expected frequencies.(using R)

A random variable X is normally distributed with a mean of 1 and variance 4. Find...

A random variable X is normally distributed with a mean of 1 and variance 4. Find a) The probability that a randomly selected score from this distribution is less than 3. a.)Sketch a normal curve and shade out the region. b) The probability that a score selected at random from this distribution lies between 2 and 5. Sketch a normal curve and shade out the region c) The probability that a score selected at random from this distribution is greater...

Questions #(3) to # (4) are based on the following information. Clooney Inc. is considering a...

Questions #(3) to # (4) are based on the following information. Clooney Inc. is considering a new product that would require an investment of $15 million. If the new product is well received, then the project would produce cash flows of $10 million a year for 3 years, but if the market does not like the product, then the cash flows would be only $4 million per year. There is a 50% probability of both good and bad market conditions....

Subjects