Suppose that X - Binomial (100, p). Consider the hypothesis test Ho : p = 0.5 versus HA: p0. Define the statistic T(X) = X and the rejection region by RR={r : |r-50| > 10}. Using the Norm %3D approximation to the Binomial distribution:

Suppose that X - Binomial (100, p). Consider the hypothesis test Ho : p = 0.5 versus HA: p0. Define the statistic T(X) = X and the rejection region by RR={r : |r-50| > 10}. Using the Norm %3D approximation to the Binomial distribution:

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

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...

See similar textbooks

Related questions

Q: Suppose that a random sample X₁, X₂,...,X20 follows an exponential distribution with parameter ß.…

Q: Let x be the observed mean of a random sample of size n from a distributionhaving mean μ and known…

A: Confidence interval on μ is given by x¯-za2σn≤μ≤ x¯+za2σn ...........(1)

Q: Suppose that a random sample X₁, X₂,...,X20 follows an exponential distribution with parameter ß.…

Q: Let a random sample of size 17 from the normal distribution N(μ, σ2) yieldx = 4.7 and s2 = 5.76.…

A: Consider the random sample size of n=17 from the normal distribution N(μ,σ2)yield x=4.7, s2=5.76.…

Q: If you think the null hypothesis is rejected in both cases, choose option c. If you think the null…

A: Given that, Xi's ~ N(μX, σ2X)Yi's ~ N(μY, σ2Y) The hypothesis for the test is, H0:μX=μY Vs…

Q: You conduct a one-way ANOVA with 5 groups and 9 subjects in each group (a balanced design). Use…

A: It is given that Number of groups k = 5 Total number of observations N = 5 × 9 = 45 For given…

Q: Assume x follow to binominal with p=4/5 and p=1/5 and n=5 , Find maximum likelihood estimator.

A: X~Binomial (n,p)p(x)=nxpxqn-x Likelihood function L(p) = ∏i=1nnxp∑xiq∑n-∑xinL(p)=k p∑xiqn2-∑xi…

Q: Use the t-distribution and the given sample results to complete the test of the given hypotheses.…

Q: Suppose tha Y is a random variable having an gamma distribution with a = 1, find the value of k such…

Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…

A: L

Q: 2. Under H, the likelihood function is given by L(1µ, a7) : A. True B. False

A: A random variable Y is said to follow the normal distribution with mean μ and variance σ2 if its…

Q: A new intern was asked to estimate a prob- ability distribution for the number of items purchased by…

A: Solution: Let X be the number of items purchased by customers entering one of the company’s retail…

Q: Give the test statistic and the p-value. Round your answer for the test statistic to two decimal…

A: Given: Ho: mu (d) =0 H1: mu (d) is not equal to 0 sample mean of d = x bar = -2.43 sample standard…

Q: Let x represent the number of mountain climbers killed each year. The long-term variance of x is…

Q: Imagine that your null hypothesis is μ = 16 and your alternative hypothesis is μ ≠ 16 for a…

A: It is given that the test is two-tailed. Level of significance is 0.05 Degrees of freedom is 19–1…

Q: Suppose a random sample of size n = 5 from a normal population gives mean = 183.1 and standard…

A: From the provided information, Sample size (n) = 5 Sample mean (x̅) = 183.1 Standard deviation (s) =…

Q: The interval (3, 15) is the 95% confidence interval for a population parameter u from a random…

A: Given Data; Confidence Interval: (3, 15) z-score for 95% Confidence interval=1.96 ME=(15+3)/2-3=6…

Q: In drilling a vertical wellbore, the spacing between major fractures are recorded. It has been found…

A: Standard normal distribution: The standard normal distribution is a special case of normal…

Q: The one-tailed test of hypothesis, H0: u = 100 versus Ha: u > 100. Suppose the test statistic is z =…

A: The one-tailed test of the hypothesis is 100. \)" data-mce-style="cursor: default;">H0:μ=100…

Q: A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal…

Q: You conduct a one-way ANOVA with 4 groups and 8 subjects in each group (a balanced design). Use…

A: Given that:A one-way ANOVA is conducted with 4 groups and 8 subjects in each group (a balanced…

Q: taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of…

Q: Excel can be used to find the critical value for an F distribution for a given significance level.…

A: First is correct you will get the same output : 2.783 ============================= 1 13…

Q: Give the test statistic and the p-value. Round your answer for the test statistic to two decimal…

A: Sample size nd=25 Sample mean xd=12.93 Standard deviation sd=13.5

Q: Using the z table, find the critical value (or values) for an α = .024 left-tailed test.

Q: A sample of n = 10 scores has a mean of M = 3. What is ΣX for this sample?

A: Solution: From the given information, M=3 and n=10.

Q: Let x represent the number of mountain climbers killed each year. The long-term variance of x is…

A: (a). 90% confidence interval for the population variance of number of mountain climbers killed each…

Q: Construct a 90% confidence interval for u-2 with the sample statistics for mean cholesterol content…

Q: A survey of the white and nonwhite population in a local area reveals the following annual trip…

A: Hypotheses for the test are given below: Test statistic for t-test: Since population standard…

Q: Use a t-distribution and the given matched pair sample results to complete the test of the given…

Q: have a variance of 1.20 x 10-4. construct a 95% confidence interval for o, the standard deviation of…

Q: Let X1, . . ., Xn be a random sample from a gamma distribution with parameters α and β. Estimate the…

A: Given that be a random sample from a gamma distribution with parameters and .

Q: For the hypothesis test Ho :µ = 16 against Hj : µ < 16 with variance unknown and n = 10, find the…

Q: Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check…

Q: Your null hypothesis is μ = 12 and your alternative hypothesis is μ ≠ 12 for a population with…

A: It is given that the mean is 12, n is 15 and the level of significance is 0.01.

Q: Let X be a random variable with mean u= E(X)=10.33 and variance o = 12.81. Determin 10 -0.800625…

A: It is given that the mean is 10.33 and the variance is 12.81.

Q: Use a t-distribution and the given matched pair sample results to complete the test of the given…

Q: Use the t-distribution and the given sample results to complete the test of the given hypotheses.…

A: Given x¯1=56, s1=8.2 n1=30 and x¯2=51, s2=6.9 n2=40

Q: general form

A: Maximum Likelihood Estimation So far, we have discussed estimating the mean and variance of a…

Q: R can be used to find the critical value for an F distribution for a given significance level. For…

A: There are 4 groups with 8 subjects in each group. α=0.10α=0.01

Q: Q1: Suppose that Y, Y2, , Y constitute a random sample from a normal distribution with known mean u…

Q: You decide to play K number of video games, where K is a Poisson random variable with parameter .…

A: Given information is; K be the number of video games K ~ P(λ) Therefore; E(K) = λ and V(K) = λ also…

Q: You decide to play K number of video games, where K is a Poisson random variable with parameter A.…

A: K = Number of video gamesK~ P(λ)P(K=k) = e-λλkk!; k=0,1,2,....E(K)=λVar(K) =λtk = time spend on a…

Q: Use the t-distribution and the given sample results to complete the test of the given hypotheses.…

Q: Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using…

Q: A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Suppose that X ~ Binomial (100, p). Consider the hypothesis test Họ : p = 0.5 versus HẠ : p + 0.5.
Define the statistic T(X) = X and the rejection region by RR={r : |r– 50| > 10}. Using the Normal
approximation to the Binomial distribution:
(a) What is a?
(b) Graph the power as a function of p.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 14 of each brand. The tires are run until they wear out. The results are given in the table below. Compute a 90% confidence interval for μA−μB assuming the populations to be approximately normally distributed. You may not assume that the variances are equal. Brand A x1=35,300 kilometers s1=4900 kilometers Brand B x2=37,200 kilometers s2=6100 kilometers
Let x1, X2, ..., Xn be a random sample from a normal population with unknown mean u and an unknown variance o?. At a given significance level a, derive the generalized likelihood ratio test for Ho : o 5. versus Completely specify the test when a = population: 0.05 and n = 26. Does the power function of the test depend on the mean of the The following `answers" have been proposed. %3B 26 (a) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 941.25. The power function of the test indirectly depends on the population mean u via = 7. (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 26 ,26 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean…
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA HB vs Ha : HA # µB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14.
q7
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and Media
R can be used to find the critical value for an F distribution for a given significance level. For example, to find the critical value (the value above which you would reject the null hypothesis) for a = 0.05 with dfbetween = 6 and dfwithin = 56, then F1-0.05 is found with: qf (1-0.05, df1=6, df2=56) Enter this code into RStudio to confirm you obtain the value 2.266. You conduct a one-way ANOVA with 4 groups and 8 subjects in each group (a balanced design). Use RStudio to find the critical values for a = 0.10 and a = 0.01 (report accurate to 3 decimal places). F1-0.10 = 4.191 X F1-0.01 = 96.694 X
Let X1, X2, ..., X, be a random sample from f(x;0) = 0e-tI(0,00)(x). Find a 100y or (1- a)100 percent confidence interval for the mean of the population.
please and thank you
Using the t-table, find the critical value for a left-tailed test with an α = 0.05 for a sample size of 23.