The values measured from a data source follow normal distribution with mean μ and standard deviation σ. Based on the 7 observed values the determined 95% confident interval for μ was [5.1,7.3].
Part 1: What is the probability that parameter μ belongs to interval [5.1,7.3]?
a. 0.05
b. 0.95
c. 0.95/sqrt(7)
d. The reasonable answer cannot be given without determining at first the prior distribution for parameter μ
Part 2: The trial was decided to repeat again. From the data source 7 new values were measured and based on which the 95% confident interval was recalculated. What is the probability that the new produced interval estimate contains parameter μ?
a. 0.05
b. 0.95
c. 0.95/7–√
d. The reasonable answer cannot be given without determining at first the prior distribution for parameter μ.
The values measured from a data source follow normal distribution with mean μ and standard deviation...
Problem I) DDT concentrations were measured in gulls. The data have a mean of 10.1 ppm and a standard deviation of 2.0 ppm. Test the hypothesis that DDT concentrations follow a normal distribution. Use a 5% level of significance DDT (ppm Z1 Number of gulls 10 36 75 72 50 7 6.0 6.0-8.0 8.0-10.0 10.0-12.0 12.0-14.0 > 14.0 2.05 1.05 0.05 0.95 1.95 2.05 1.05 0.05 0.95 1.95 What's the probability of finding DDT concentration less than or equal 6.0ppm?...
Suppose a random sample of 17 is selected from a normal distribution and the sample mean x-bar = 102.5 and the sample standard deviation Sx = 4.3. Is this a z distribution or a t distribution? A. t distribution with 17 degrees of freedom B. t distribution with 16 degrees of freedom C. z distribution D. Cannot be determined Part b construct a 96% confidence interval for the population mean A. 100.17 to 104.83 B. 100.36 to 104.64 C. 100.00...
10. Based on a random sample of size 7 from a normal distribution with mean y, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta for specific combinations of a and v: v=6 v = 7 a=0.1 a = 0.05 a= 0.025 1.440 1.943 2 .447 1.4151.8952.365 If we want to...
10. Based on a random sample of size 7 from a normal distribution with mean u, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta, for specific combinations of a and v: a=0.1 1.440 1.415 a= 0.05 1.943 v=6 v=7 a= 0.025 2 .447 2.365 1.895 If we want to be...
QUESTION #1 Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 4; σ = 6 P(1 ≤ x ≤ 10) = QUESTION # 2 In a certain article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of...
2. (10pts) The following 16 random samples; 5.33, 4.25, 3.15, 3.70, 1.61, 6.40, 3.12, 6.59,3.53, 4.74, 0.11, 1.60, 5.49, 1.72, 4.15, 2.30, came from normal distribution with mean μ and variance σ2, i.e., Xi, X2' .. . , X16 ~ N(μ, σ*), with the density function (a) (4pts) Find the maximum likelihood estimates of μ and σ2, denoted with μ and σ2. (b) (4pts) Based on above μ and σ2, construct 95% confidence intervals for μ and σ2 separately. (c)...
5. Suppose X follows a normal distribution with mean u = 200 and standard deviation o = 40. Find each of the following probabilities. (8 points) a. P(160 < x < 232) b. P(X > 160) C. P(X < 100) d. P(230 < x < 284) 6. Sup Suppose we know that SAT scores have a population average u = 1080 and a standard deviation o = 200. A university wants to give merit scholarships to all students with an...
1. For power sources from Warehouse A, we know that the voltage of each power source is independent of the others and is Gaussian with mean 10 and variance 1. Let the voltage of the 20 power sources in a given shipment be denoted by Xi, X2,... X20- [7] (a) Suppose we put the 20 power sources from a given shipment from Warehouse A in series. Find an interval (a, b) such that the total voltage Y-222, Xi is within...
Confidence Interval about a Population Standard Deviation 3) Consider the same information as in Example 2 on page 336, section 7.3, but use a confidence level of 90% instead of 95% Write your solution just like in the example. Show all work and use the formulas (do not use any technology here!) Note that the solution shown in the example is quite detailed. Your solution could be shorter, start where it says Using Table A-4 on page 337, and continue...
problems 4, 5, 6, 11 and 13
If the population standard deviation was doubled to 10.4 and the level of confidence remained at 90%, what would be the new margin of error and confidence interval Margin of error, E. Confidence interval: 20.11<x<34.31 O Did the confidence interval increase or decrease and why? increase 4. Definition of Confidence Intervals (Section 6.1) Circle your answer, True of False. • A 99% confidence interval means that there is a 99% probability that the...