Consider a normal population distribution with the value of σ known.
(a) What is the confidence level for the interval x ±
2.88σ/sqrt(n) ? (Round your answer to one decimal
place.)
___________%
(b) What is the confidence level for the interval x ±
1.42σ/sqrt(n) ? (Round your answer to one decimal
place.)
___________%
(c) What value of zα/2 in the CI
formula below results in a confidence level of 99.7%? (Round your
answer to two decimal places.)
( x − zα/2 ·σ/sqrt(n), x + zα/2 ·σ/sqrt(n) )
zα/2 = ____________
(d) Answer the question posed in part (c) for a confidence level of
78%. (Round your answer to two decimal places.)
zα/2 = ________
You may need to use the appropriate table in the Appendix of Tables
to answer this question.
Solution :
(a) given confidence interval is x +/- 2.88σ/sqrt(n)
=> P(-2.88 < z < 2.88) = 0.996 = 99.6%
=> the confidence level is 99.6%
(b) given confidence interval is x +/- 1.42σ/sqrt(n)
=> P(-1.42 < z < 1.42) = 0.8444
= 84.44%
= 84.4% (rounded)
(c)
=> for 99.7% confidence interval , Z = 3.00
=> zα/2 = 3.00
(d)
=> for 78% confidence interval , Z = 1.23
=> zα/2 = 1.23
Consider a normal population distribution with the value of σ known. (a) What is the confidence...
Consider a normal population distribution with the value of o known. (a) What is the confidence level for the interval x 2.810/ n? (Round your answer to one decimal place.) % (b) What is the confidence level for the interval + 1.450/ n? (Round your answer to one decimal place.) % (c) What value of zul in the CI formula below results in a confidence level of 99.7%? (Round your answer to two decimal places.) (8–2012. o. X + 22...
Consider a normal population distribution with the value of a known. (a) What is the confidence level for the interval 72.850/Vn? (Give answer accurate to 1 decimal place.) % (b) What is the confidence level for the interval 7+20/vi? (Give answer accurate to 1 decimal place.) % (c) What value of 2a/2 in the Cl formula results in a confidence level of 92.4%? (Give answer accurate to 2 decimal places.) (d) Answer the question posed in part (C) for a...
Consider a normal population distribution with the value of known. a) What is the confidence level for the interval (i) x 1.96 n (ii) x 2.65 n (iii) x 3.34 n b) What value of z in the confidence interval formula x z n x z n 2 2 , results in a confidence level of (i) 97.96% (ii) 78.88% (iii) 99.94% c) Would a 90% C.I. be narrower...
PLEASE SHOW ALL THE WORKING Consider a normal population distribution with the value of known. a) What is the confidence level for the interval (i) x 1.96 n (ii) x 2.65 n (iii) x 3.34 n b) What value of z in the confidence interval formula x z n x z n 2 2 , results in a confidence level of (i) 97.96% (ii) 78.88% (iii) 99.94% c) Would...
A population is normal with known standard deviation σ. What is the confidence level corresponding to this confidence interval for μ? Confidence interval: Xbar - σ/√n < Xbar < Xbar + σ/√n
PLEASE ANSWER BOTH QUESTIONS, THIS IS MY THIRD TIME POSTING THIS SET AND THEY HAVE ANSWERED WRONG every single time. please i am begging you, i will rate you!!! The breaking strength of a rivet has a mean value of 9.900 pai and a standard deviation of 500 p a what is the probability that the sample mean breaking strength for a random sample of 40 rivets between 9,800 and 10 00 (Round your ins etofaraon spaces) (b) If the...
a.Construct the confidence interval for the population mea μ. c=0.98 x=16.3, σ=5.0, and n=95 A 98% confidence interval for μ is ( ___ , ___ ) (Round to one decimal place as needed. b. Find the critical value tc for the confidence level c=0.98 and sample size n=13. tc= _____ (Round to the nearest thousandth as needed.) c. Find the margin of error for the given values of c, s, and n.c=0.80, s=4, n=28 The margin of error is _____...
Construct the confidence interval for the population mean μ c: 0.95, x-16.8, σ: 9.0, and n-100 A 95% confidence interval for μ is OD (Round to one decimal place as needed.) 6.1.27 Use the confidence interval to find the margin of error and the sample mean (1.58,2.06) The margin of error is (Round to two decimal places as needed) 6.1.31 Find the minimum sample size n needed to estimate μ for the given values of c, o, and E. cz...
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies.The confidence level is 90%, σ=3347 thousand dollars, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is as shown.Select the correct choice below and, if necessary, fill in the answer box to...
Determine the t critical value for a two-sided confidence interval in each of the following situations. (Round your answers to three decimal places.) (a) Confidence level = 95%, df = 10 (b) Confidence level = 95%, df = 15 (c) Confidence level = 99%, df = 15 (d) Confidence level = 99%, n = 5 (e) Confidence level = 98%, df = 22 (f) Confidence level = 99%, n = 38 You may need to use the appropriate table in...