Which of the following statements are true? A. The interval X^- plusminus 1.96.s

Question

Which of the following statements are true? A. The interval X^- plusminus 1.96.sigma/squareroot n is random, while its width is not random B. The interval X^- plusminus 1.96.sigma/squareroot n is not random, while its width is random C. The interval x^- plusminus 1.96.sigma/squareroot n is random, while its width is not random D. The interval x^- plusminus 1.96.sigma/squareroot n is not random, while its width is random. E. None of the above statements are true. Which of the following statements are not true? A. A correct interpretation of a 100 (1-alpha)% confidence interval for the mean mu relies on the long-run frequency interpretation of probability. B. It is correct to write a statement such as P[mu lies in the interval (70, 80)] = .9.5 c. The probability is .95 that the random interval X^- plusminus 1.96 middot sigma/squareroot n includes or covers the true value of mu. D. The interval x^- plusminus 1.645 middot sigma/squareroot n is a 90% confidence interval for the mean mu. E. None of the above statements are true. If the width of a confidence interval for mu is too wide when the population standard deviation sigma is known, which one of the following is the best action to reduce the interval width? A. Increase the confidence level B. Reduce the population standard deviation sigma C. Increase the population mean mu D. Increase the sample size n E. None of the above answers are correct. A random sample of 10 observations was selected from a normal population distribution. The sample mean and sample standard deviations were 20 and 3.2, respectively. A 95% prediction interval for a single observation selected from the same population is A. 20 plusminus 6.152 B. 20 plusminus 4.244 C. 20 plusminus 7.962 D. 20 plusminus 7.592 E. None of the above answers are correct.

Explanation / Answer

6) We know that

Z = (X-x / s/sqrt(n))

X = x + Z * s / sqrt(n)

s - standard deviation

Mean can be any value based on its deviation from , but width depends omn standard devaition

hence confidence intervals are fixed with a given formula, but width can vary

option D

7)

a) long run frequency is stable, hence we use it for calculations

b) The format is not appilcable

N(u,s)

p(X operator Z ) should be used

c,d) are the definitions of ccentral limit theorem

Option B

8)

Z = dX * sqrt(n) / s

s = dX *sqrt(n) / Z

As n decreases s decreases

Increase in CI increases the width

eg,. at alpha = 0.95, Z = 1.96, at alpha = 0.99, Z = 2.576

population standard deviation decrease causes reduces the width (CI).

CI = x+ s*Z /sqrt(n)

reducing the population mean increases the width

If the sample size is increases, there are more percentage of items falling into critical and acceptance region increases and CI increases proportionately

9)

given mean (x) = 20

standard devaition (s) = 3.2

sample observations (N) = 10

CI = x +/- Z * s/sqrt(n)

= 20 +/- 1,96 * 3.2 / sqrt(10)

= 20 +/- 1.983

OPTION E)

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