**Title: Hypothesis Testing for Compressive Strength of Cement Mixtures**A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 kN/m². The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 69. Let μ denote the true average compressive strength.### (a) Null and Alternative Hypotheses#### What are the appropriate null and alternative hypotheses?- **Option 1:** - $ H_0: \mu \leq 1,300 $ - $ H_a: \mu > 1,300 $ (Correct)- Other options incorrectly set up $ H_0 $ and $ H_a $.### (b) Probability Distribution and P-Value Calculation#### Let $ \bar{X} $ denote the sample average compressive strength for $ n = 15 $ randomly selected specimens. Consider the test procedure with test statistic $ \bar{X} $ itself (not standardized). What is the probability distribution of the test statistic when $ H_0 $ is true?- **Correct Answer:** The test statistic has a normal distribution.#### P-Value CalculationIf $ \bar{X} = 1,340 $, find the P-value (rounded to four decimal places).- **P-value = 0.01**Should $ H_0 $ be rejected using a significance level of 0.01?- **Decision:** Do not reject $ H_0 $### (c) Distribution of Test Statistic for Different Mean#### What is the probability distribution of the test statistic when $ \mu = 1,350 $ and $ n = 15 $?- **Correct Answer:** The test statistic has a normal distribution.#### Mean and Standard Deviation- **Mean = 1350 kN/m²**- **Standard Deviation = 17.808 kN/m²**#### Type II Error ProbabilityFor a test with $ \alpha = 0.01 $, what is the probability that the mixture will be judged unsatisfactory when in fact $ \mu = 1,350 $ (a type II error)?- **Probability = 0.1721**This exercise illustrates the application

Answered: (a) What are the appropriate null and…

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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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m². The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o = 67. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ 1,300 H₂: μ = 1,300 Ho: μ = 1,300 H a: μ> 1,300 ○ Ho: μ = 1,300 H₂: μ< 1,300 (b) Let X denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. O The test statistic has a binomial distribution. The test statistic has a normal…
The cooling system in a nuclear submarine consists of an assembly of welded pipes through which a coolant is circulated. Specifications require that weld strength must exceed 150 psi. A random sample of 20 welds resulted in a sample mean of 153.7 psi and a sample standard deviation of 11.3 psi. Which side(s) is (are) the critical region(s) located? O left side Oright side O both left and right sides O neither left nor right since there is no critical region
= Consider a test of Ho: M₁ = μ₂ versus Ha: M₁ > µ₂ using the sample results ₁ $2 8.16 with n₂ = 24. What value is closest to the p-value for this test? = 0.0014 0.052 0.104 0.948 82.3, $1 = 7.54 with n₁ = 28 and 2 = 78.6,
3. (Sample size determination for hypothesis testing) Suppose that X₁,..., Xn N(μ, o2) and o² is known. We would like to test We consider the test statistic Ho: μ = po, and the critical region at significance level a 1- {=; C = T = X x; x > µo + %α² H : μ > μο· B(μ') = = (a) We write ß(µ') to be the probability of type II error given the true value of µ = µ'. Prove that 0 (za + 10 = 1²). where Þ(z) = P(Z ≤ z) is the cdf of Z ~ N(0,1). 1 n = = O 2.2.d. (b) We would like to determine the sample size n so that the probability of type I error is a and the probability of type II error is ß. Using part (a), prove that 2 - ( 0¹ (²0 + zp)) ². Po - (c) Let u denote the true average tread life of a certain type of tire. Consider testing Ho : μ = 25,000 versus H₁ : μ> 25, 000 from a normal population distribution with o = 1300. Assuming the true value of μ is μ' = 24,000. What is the sample size n so that the probability of type I error is a = 0.05 and the probability of type II error is = 0.025?
11
t and p-value please. WILL thumbs up if correct.
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We wish to test the null hypothesis that the proportion of cancer deaths among people exposed to radioactive fallout in Utah in 1955 is equal to 0.15 versus the alternative hypothesis that the proportion differs from 0.15 using alpha = 0.05. What is the region of rejection for this test for sample of size 20? Reject Ho if y in { LISTY VALUES HERE }
Calculate the test statistic x'and state your decision regarding the null hypothesis. 23. It has been rumored that the color distribution of M&M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. Color Brown Yellow Red Orange Blue Green Total Observed 27 16 21 12 15 100 Provided the assumptions of the test are satisfied, calculate the test statistic 7. a) 4.15, Reject H, b) 4.15, Fail to Reject H, c) 16.83, Reject H, d) 16.83, Fail to Reject H,

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