Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is whichvaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 75recipients of vaccine X and 83 recipients of vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 129. Thevaccine Y recipients had a mean 6AEQ of y = 133. It is recognized that the true standard deviation of 6AEQ forvaccine X recipients is a = 9.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Yrecipients is σy = 10.7. The true (unknown) mean 6AEQ for vaccine X recipients is x, while the true (unknown)mean 6AEQ for vaccine Y recipients is My. 6AEQ measurements are known to be a normally distributed. Insummary:Type Sample Size Sample Mean Standard DeviationVaccine X 75129Vaccine Y 831339.710.7a)Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 75 vaccineX recipients.b)Calculate the variance of the random variable Y, which is the mean of the 6AEQ measurements of the 83 vaccineY recipients.c) Calculate the variance of X-Y?d) Calculate the standard deviation of X-Y?e) If we wish to create an 94% confidence interval for x - y then what is the z criticall vallue used?f)Create an 94% confidence interval for Mx Hy. (|g) What is the length of your 94% confidence interval for Mx Hy?h) If we used this data to test Ho: x - y =0 against the alternative H xHy <0 then what would the valueof the calculated test statistic z have been?i) If we used this data to test Ho: Mx - y =0 against the alternative Ha: Mx - My <0 then what would the p valuehave been?j)If we used this data to test Ho: x - y =0 against the alternative Hai Mx - My #0 then what would the p valuehave been?

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Answered: Suppose there are two different…

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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Scores on a certain "IQ" test for 18-25 year olds are normally distributed. A researcher believes that the average IQ score for students at a certain NJ college is less than 110 points, and so wants to test this hypothesis. The researcher obtain a SRS of 45 student IQ scores from school records and found the mean of the 45 results was 108 with a sample standard deviation of 21. The level of significance (alpha) used for this problem is 0.05. What is the appropriate test statistic (Student must complete by showing by formula using the ap- propriate values in that formula "showing work" and the final answer and appropriate label)? O T test score = (108-110)/(21/sqrt(45)) = -.639 T test score (108-110)/(21/sqrt(45)) = .639 %3D OT test score = (110-108)/(21/sqrt(45)) = .639 %3D T test score (108-110)/(45/sqrt(21)) =-.2037 %3D 素

Suppose that there are two borrowing strategies from a commercial bank as short-term and long-term. We have two small samples (n1=8 and n2=8) and sampled populations are normal. Standard deviation for the first sample is 200 and for the second one is 150. The researcher wants to determine whether the variation in the customers preferring short-term borrowing differs from the variation in the customers preferring long-term borrowing. (Use 0.10 significance level)
The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?2 = 0.18 mm2. An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.28 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.00 Find a 90% confidence interval…
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A laboratory claims that the mean sodium level, u, of a healthy adult is 143 mEq per liter of blood. To test this claim, a random sample of 50 adult patients is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 10 mEq. Can we conclude, at the 0.1 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)
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chester butchery supplies vienna sausages in the entire kzn province. a meat packer is investigating the marked mass shown on vienna sausages. a pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. how many packs should be sampled in order to be 92% confident that the sample mean will differ by at most 0.2kg.
Aresearcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 14 blue crabs from Location A contain a mean of 194 milligrams of fish and a standard deviation of 39 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 187 milligrams of fish and a standard deviation of 44 milligrams. Al a 0 10, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: H-220 O B. Ho H-2 0 (b) Find the standardized test statistic for u - t=0.381 (Round to three decimal places as needed) Enter your answer in the answer box and then click Check Answer parts remaining Clear All Check Answer leste ppt_08_03.pptx Open file Show all P Type here to search 235 PM 2/21/2021 ts fho sk hz home end insert delet esc & @…
Scores on a certain "IQ" test for 18-25 year olds are normally distributed. A researcher believes that the average IQ score for students at a certain NJ college is less than 110 points, and so wants to test this hypothesis. The researcher obtain a SRS of 45 student IQ scores from school records and found the mean of the 45 results was 108 with a sample standard deviation of 21. The level of significance (alpha) used for this problem is 0.05/ What is the appropriate test statistic (Student must complete by showing by formula using the ap- propriate values in that formula "showing work" and the final answer and appropriate label)? O T test score = (108-110)/(45/sqrt(21)) = -.2037 O I test score = (108-110)/(21/sqrt(45)) = -.639 T test score = (108-110)/(21/sqrt(45)) = .639 I test score = (110-108)/(21/sqrt(45)) = .639

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