8.2.3. Consider a normal distribution of the form N(0,4). The simple hypothesisHo 0 0 is rejected, and the alternative composite hypothesis H₁:0> 0 isaccepted if and only if the observed mean of a random sample of size 25 is greaterthan or equal to. Find the power function (), 0≤0, of this test.

Given that X is distributed N(θ, 4) H0: θ=0 and H1: θ>0 Sample size (n) = 25 Rejection region:…

Answered: 8.2.3. Consider a normal distribution…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1/7.dO 14 Juel If X is random variable with parameter mean = 3 variance = 9 find 7... Find P(x> 0) 0.8413.a C 0.5 0.99 .c 0.4.d C
H3.
4.52 Random variables X and Y follow a joint distribution f(x, y) = = 2, 0< x≤y< 1, otherwise. 0, Determine the correlation coefficient between X and Y.
2.2. Let Y₁, Y₂Yn denote a random sample from a gamma distribution with each Y-gamma (0; B) with known. Find a sufficient statistic for 8.
Q2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Ос
I need help with this one, please. I need it to be step-by-step please for me to understand.
112.1 and o = 61.4. You intend to draw A population of values has a normal distribution with µ a random sample of size n = 212. a. Find P34, which is the score separating the bottom 34% scores from the top 66% scores.P34 (for single values) = b. Find P34, which is the mean separating the bottom 34% means from the top 66% means. P34 (for sample means) = Round to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.
Q2
Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(
8.3
25. Each of a random sample of 30 student nurses who participated in a research project was given a test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400? Let α = 0. 05 and assume that the population is normally distributed. (A) Yes (B) No

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