**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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iven ˆpp^ = 0.2857 and N = 35 for the high income group,Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.1 significance level.a) Identify the correct alternative hypothesis: p>.50p>.50 p<.50p<.50 μ=.50μ=.50 p=.50p=.50 μ<.50μ<.50 μ>.50μ>.50 Give all answers correct to 3 decimal places.b) The test statistic value is: c) Using the P-value method, the P-value is: d) Based on this, we Reject H0H0 Fail to reject H0
\multicolumn2|c|Regression Statistics Multiple R R Square Adjusted R Square 0.6365 0.4051 0.289 Standard Error 5.65 Observations 50 ANOVA df SS MS F Significance F Regression 8 890 111.25 3.49 0.00369246 Residual 41 1307 31.88 Total 49 2197 Determine each of the following from the output: R2| = Se = MSR =
Considering that k= 4, n= 58, SSE= 84.75, and SSR= 725 fill in the ANOVA table and state the results of testing the stated Null Hypothesis below DF SS MS Significance Regression 0.455 Residual From the table F= 2.55 Total Họ. by = 0 the result of testing the Null Hypothesis is
A population of values has a normal distribution with u = 94.8 and o = 16. You intend to draw a random sample of sizen = 76. Find the probability that a sample of size n = 76 is randomly selected with a mean greater than 100.3. P(M > 100.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z- Scores rounded to 3 decimal places are accepted. Submit Question % & 3 4. 7 9. e y 00 %24 CU
IDENTIFY ITS TEST STATISTIC (Chi-square, t-test, z-test, ANOVA) 1. What is the degrees of freedom Given: n = 45 x = 12 H.:µ = 15 H = 15 Ha: µ # 15 o = 7.5 2. What is the p-value Given: n = 30 H,:µ = 28 x = 25 s = 5 Ha: μ< 28 H = 28 |
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In Thunder Bay, during the month of June, afternoon thunderstorm rainfall frequently occurs. Based on the assumption that in Thunder Bay, there is a 20% chance of occurrence of a thunderstorm rainfall on any day of the month of June, compute the probability of having 5 days free of thunderstorm rainfall in Thunder Bay. What is the probability of one rainy day during the 5 days? (a) Compute the area under the standard normal curve for the following cases: (a) between z = 0 and z = 1.5, (b) z = -1.5 and z = 0, and (c) between z = - 0.5 and z= 2.5. (b) The probability of a flood event occurring every year is 0.4. What is the probability of this event occurring in year 2 and not in year 1? (c) What is the probability that a 5-year flood will occur three times in a period of 10 years? What is the probability that it will occur at all? How many floods of this magnitude will occur, on average, during the 10 years?
For X ~ normal with µ = 2, o = 3 and a sample size of 38, P(X < - 1) = Note: round your z score to two decimals places
From the data we find that Sxx = 0.11273, Syy = 11,807,324,805, Sxy = 34,422.28. n=29, test the null hypothesis that p = 0.9 against the alternative that p > 0.9. Use a 0.05 level of significance. Use 2 decimal places for the answers. Critical Region: z> Test statistic: Z = P-value: p= Decision: There is certainly some evidence that the correlation coefficient does not exceed 0.9. True or False? Type T or F for the answer.
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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