a)
(ybar - t * s/sqrt(n) , ybar + t* s/sqrt(n))
df = n-1 = 9
t =
2.262157 |
(20 - 2.2622 * 4/sqrt(10) , 20 + 2.2622 * 4/sqrt(10))
=( 17.1385 , 22.8615)
b)
for n = 1000
df = 999 , t = z = 1.96
(20 - 1.96* 4/sqrt(1000) , 20 + 1.96* 4/sqrt(1000))
=( 19.7520 , 20.2479)
c)
answer to a) would change
but not for b) part
as n = 1000 > 30
by central limit theorem , we can approximate by normal distribution
Please rate
5. Suppose we obaerve Y. ..Y, from a normal distribution with unknown parameters such that P...
5. Suppose we observe Y Yn from a normal distribution with unknown parameters such that ' 20, s2 = 16, and n= 10. (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the sarne value of P and 8. Find a 95% confidence interval for μ. (c) Would your answer to (a) or (b) change if the data were not from a normal distribution?
6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y 24, s2 36, and n 15. (a) Find the rejection region of a level α-0.05 test of H0 : μ-20 vs. H1 : μ * 20. Would this test reject with the given data? (b) Find the rejection region of a level α -0.05 test of Ho : μ < 20 vs. H1 : μ > 20 would this test reject with the given...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
3. Suppose that the random variable X is an observation from a normal distribution with unknown mean μ and variance σ (a) 95% confidence interval for μ. (b) 95% upper confidence limit for μ. (c) 95% lower confidence limit for μ. 1 . Find a
7.5 Suppose you draw a random sample of size n from a normal distribution with unknown mean u and known standard deviation o and construct a 95% confidence interval for u. If you want to halve the margin of error, how much larger would the sample size have to be?
(1 point) Suppose that the random variable Y has a gamma distribution with parameters a = 2 and an unknown B. Show that 2Y/B has a xa distribution with 4 degrees of freedom. Using 2Y/B as a pivotal quantity, derive a 97% confidence interval for B. Suppose that Y = 19.6. What is the resulting 97% confidence interval for B? <B<
(21) A sample of size 20 is drawn from a normal distribution with unknown variance and mean. The sample variance s2 = 0.012. Find a 95% two-sided confidence interval for the standard deviation o of the population. A. [0.0833,0.1600] B. (0.010,0.0130] C. (0.0069,0.0256] D. None of the above
8.40 stion 4 (6 pt) (Ex. 8.40 on page 409 is modified): Suppose that random variable Y is an observation from a normal distribution with unknown mean u and variance l Find and verify a pivotal quantity that you can use to derive confidence limits for the mean u. Find a 95% lower confidence limit for. a. b. 8.40 Suppose that the random variable Yis an observation from a normal distribution with unknown mean μ and variance 1 . Find...
Let Ybe a normal random variable with parameters (1,a2). In other words, its mean is 1 while its variance a2 is unknown. Find 95% upper one-sided confidence interval for a2 in terms of Y Let Ybe a normal random variable with parameters (1,a2). In other words, its mean is 1 while its variance a2 is unknown. Find 95% upper one-sided confidence interval for a2 in terms of Y
We have a random sample of size 17 from the normal distribution N(u,02) where u and o2 are unknown. The sample mean and variance are x = 4.7 and s2 = 5.76 (a) Compute an exact 95% confidence interval for the population mean u (b) Compute an approximate (i.e. using a normal approximation) 95% confidence interval for the population mean u (c) Compare your answers from part a and b. (d) Compute an exact 95% confidence interval for the population...