A sample of size 81 is taken from a population with unknown mean and standard deviation 4.5.In a test of Ho: M = 5 vs. H₂: μ<5, if the sample mean was 4, which of the following is true?(i) We would fail to reject the null hypothesis at a = 0.01.(ii) We would fail to reject the null hypothesis at a = 0.05.ii) We would fail to reject the null hypothesis at a = 0.10.both (ii) and (iii)O only (i)both (i) and (ii)all of themonly (iii)●mMAWP

That is, there is no evidence to conclude that the population mean is less than 5.That is, there is…

Answered: A sample of size 81 is taken from a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a lake pollution study, the concentration of lead in the upper sedimentary layer of a lake bottom is measured from 25 sediment samples. The sample mean and the standard deviation of the measurements are found to be 0.38 and 0.06, respectively. Suppose Ho : u = 0.34 H1: u# 0.34 (a) State Type I and Type Il errors. (b) Conduct a hypothesis test at 0.01 level of significance by doing the seven-step classical approach. (please show all seven steps, formulas, calculations and the curve)
A company is doing a hypothesis test on the variation of quality from two suppliers. Both distributions are normal, and the populations are independent. use a = 0.01 2 H0:01 HA: 01 > 2 2 02² 10₂² The standard deviation of the first sample is 2.2077 5.1485 is the standard deviation of the second sample. The test statistic is =
A random sample of 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 11. An independent random sample of 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 13. Test the claim that the population means are different. Use level of significance 0.01.
Two independent samples have been selected, 7777 observations from population 1 and 5858 observations from population 2. The sample means have been calculated to be ?⎯⎯⎯1=13.4x¯1=13.4 and ?⎯⎯⎯2=11.3x¯2=11.3. From previous experience with these populations, it is known that the variances are ?21=27σ12=27 and ?22=29σ22=29. For the hypothesis test of ?0:(?1−?2)=1.8H0:(μ1−μ2)=1.8 and ??:(?1−?2)≠1.8Ha:(μ1−μ2)≠1.8 Use ?=0.04α=0.04. (a) Compute the test statistic. ?=z= (b) Find the approximate p-value?−?????=p−value= The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8. B. We can reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8 and accept that (?1−?2)≠1.8(μ1−μ2)≠1.8.
To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 35. (Use the 4-step procedure to conduct the hypothesis test) If the sample variance is s2 = 32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05? If the sample variance is s2 = 72, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05? Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?
A sample of n=18n=18 data values randomly collected from a normally distributed population has variance s2=24.6s2=24.6. We wish to test the null hypothesis H0:σ2=64H0:σ2=64 against the alternative hypothesis H1:σ2<64H1:σ2<64 at a significance of α=0.01α=0.01. What is the value of the test statistic? Write your answer rounded to 3 decimal places. What is the critical value? Write your answer rounded to 3 decimal places.
From 2012-2017 the 5 year remission rate of Breast cancer was 91%. Suppose we wish to know if that percentage has changed in 2020. We take a random sample of 360 breast cancer survivors from 2015-2020 and find out that 315 have remained in remission since. Use a significance level of α = .05. (a) State the null and alternate hypothesis (b) Can we continue with testing the hypothesis? Why or why not? (c) If possible, proceed with the hypothesis test and reach a conclusion.
Suppose that we have a problem for which the null and alternative hypothesis are given by: H0: μ = 890. H1:μ ≠ 890. Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.09.

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