Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octanenumber for formula 1 is o? = 1.5, and for formula 2 it is o,the mean octane numbers observed are = 89.5 fluid ounces and I2 = 93.1 fluid ounces. Assume normality.= 1.2. Two random samples of size n1 =15and n2 = 20 are tested, and(a) Test the hypotheses Ho : H1H2 versus H1 : µ1 < µ2 using a = 0.05. Round your answer to three decimal places (e.g. 98.765).%|Zov Ho.(b) Calculate a 95% two-sided confidence interval on the mean difference road octane number, x1 – X2. Round your answer to threedecimal places (e.g. 98.765).

In order to determine whether the mean octane number for formula 2 is significantly greater than…

Answered: Two different formulas of an oxygenated…

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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Two different formulations of an oxygenated motor fuel are being tested to study their roadoctane numbers. The variance of road octane number for formulation 1 is σ1 2 = 1.5, and for formulation, 2 it is σ2 2 = 1.2 . Two random samples of size n1 = 15 and n2 = 20 are tested, andthe mean road octane numbers observed are x̅1 = 89.6 and x̅2 = 92.5. Assume normality.(a) If formulation 2 produces a higher road octane number than formulation 1, themanufacturer would like to detect it. Formulate and test an appropriate hypothesis using α =0.05.
An auto manufacturer claims that the variance of the gas mileage in a model of a hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At alpha = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.
Given that age of ECU students is normally distributed. A random sample of 16 students had an average age of 25 years and a variance of 4 square years. The 98% CI for the true average age of all ECU students is?
The blood pressure and weight of Jellystone Park bears are correlated with and .6 is the correlation coefficient of blood pressure with weight. The average blood pressure is 150 with variance 100, for Jellystone Park bears. For a randomly selected bear if we predict its blood pressure is 150 before weighing it, what is our expected squared error?
The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At alpha equals0.05 , can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.64 0.33 0.44 0.35 2.73 1.33 0.51 0.42 0.34 1.53 0.75 nothing 0.48 0.58 nothing 0.47 1.38 nothing (a) Identify the claim and state Upper H 0 and Upper H Subscript a . Choose the correct answer below. A. Upper H 0 : mu 1 equals mu 2 equals mu 3 (claim) Upper H Subscript a : At least one mean is different from…
The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At alpha equals0.01 , can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.35 0.42 0.44 0.51 2.74 1.28 0.64 0.46 0.34 1.62 0.33 nothing 0.47 0.75 nothing 0.36 1.32 nothing (a) Identify the claim and state Upper H 0 and Upper H Subscript a . Choose the correct answer below. A. Upper H 0 : At least one mean is different from the others. (claim) Upper H Subscript a : mu 1 equals mu 2 equals…
Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. What is the variance of the sample mean Xn?
A new material is being tested for use in the manufacture of electrical conduit, to determine whether it will reduce the variance in crushing strength over the old material. Crushing strengths are measured for a sample of size 16 of the old material and a sample of size 20 of the new material. If it is shown that the crushing strength with the new material has smaller variance, the new material will be used.
Two samples of sizes 25 and 20 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom of the equal-variances t-test statistic is ?
If a set of data is normally distributed with a mean of 20 and a variance of 16, a z-score of -3.8 would convert into what raw score?
Rosner analyzed data from children who lived near a lead smelter (which is a facility that uses extreme heat to extract the metal lead from lead ore) in El Paso, Texas, and reported that out of 124 children studied, 23 developed colic (which is a pattern of fussiness and crying for no apparent reason). Suppose that in the state of Taxes in general at the time (early 1980s), the rate of colic in children was 16.0%. Follow the steps for testing whether the proportion of children developing clico was significantly different for the 124 children living near the lead smelter than for Taxes children in general (16%). Use alpha level of 0.03 a. Identify the null hypothesis for this statistical test. b. Identify the alternative hypotheses for this statistical test. c. Explain: Why should this be a two-tailed test, the way I have described it? d. calculate the sample proportion p̂, rounded to three decimal places. e. Calculate the appropriate test statistic, show all work. f. Based on…
. A taxi company has been using Brand A tires, and the distribution of kilometers to wear-out has been found to be approximately normal with mean =114,000 and σ = 11,600. Now it tries 12 tires of Brand B and finds a sample mean 117,200. Test at the 5% level of significance to see whether there is a significant difference (positive or negative) in kilometers to wear-out between Brand A and Brand B. In the problem above, if the true kilometers to wear-out is 114,000, what is the 95% confidence interval for sample means? First show how to get the critical z values.

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