In a lake pollution study, the concentration of lead in the upper sedimentary layer of a lake bottom ismeasured from 25 sediment samples. The sample mean and the standard deviation of the measurementsare found to be 0.38 and 0.06, respectively. SupposeHo : u = 0.34H1: 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)

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Answered: In a lake pollution study, the…

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 company claims that the mean monthly salary for their managers is 8 thousand dollars.A sample of 100 managers has a mean monthly salary of 7.5 thousand dollars with a standard deviation of 1.9 thousand dollars. You want to perform a hypothesis test challenge the validity of the claim made by the company, at a significance level of α=0.10α=0.10. Your hypotheses are:Ho:μ=8,000Ho:μ=8,000Ha:μ<8,000Ha:μ<8,000 (a) Find the test statistic, rounded to 4 decimal places.Test Statistic = (b) FInd the p-value, rounded to 4 decimal places.p-value =
(3) A process for manufacturing soft soda produces normally distributed yield with a mean of 600 and a standard deviation of 100 units. A new modified process yields an average of 630 units for a sample of size 50. At a = 0.05 does the modified process increase the yield? %3D
3) A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times, with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With a substrate concentration of 2.0 moles per liter, 12 runs were made, yielding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances
Data provided by the National Association of College Employers indicated that the average starting salary for graduates with a Bachelors Degree in Accounting was $37,000 in 2008. In June 2010 a sample of 48 graduating accounting majors provided a sample average starting salary of $38,100, with a sample standard deviation of $5200. Conduct a hypothesis test to determine if it can be assumed that accounting graduates in 2010 had higher average salaries than graduates in 2008, using α = .05.
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 65 feet, with a population standard deviation of 13.6. The mean braking distance for SUVS equipped with tires made with compound 2 is 69 feet, with a population standard deviation of 8.5. Suppose that a sample of 55 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ₁ be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 3 of 5 Find the p-value associated with the test statistic. Round your answer to four decimal places. Answer How to enter your answer (opens in…
Currently patrons at the library speak at an average of 61 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 57 people speaking at the library. Their average decibel level was 63.8 and their standard deviation was 9. What can be concluded at the the αα = 0.10 level of significance?
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1067 hours and a standard deviation of 137 hours. A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours. The significance level is 5%. Assume the population is normally distributed. What is the critical value of t? O-2.787 O-1.711 O-1.704 -2.797 What is the value of the test statistic, t, rounded to three decimal places? What is the p-value for this hypothesis test, rounded to four decimal places? Should you reject or fail to reject the null hypothesis in this test? Does the data provide evidence to contradict the company's claim about the average lifetime of their light bulbs?
In a study of the invasive species heracleum mantegazzium, Jan Pergl and associates compared the density of these plants in their native area in Russia and in an invaded area of the Czech Republic. In their native area, the average density was well-established as μ = 5 plants per square meter. In an invaded area, a sample of n = 60 plants produced an average density of x = 11.117 plants per square meter with a sample standard deviation of s = 2.37 plants per square meter. Using a signficance level of α = 0.01, is there sufficient evidence to conclude that the density of the species in the invasive area is significantly higher than in the native area? Use the hypothesis-testing framework to answer this question. Be sure to state both the null and alternative hypothesis, calculate a test statistic, and state the conclusion in non-technical terms. You may use either the P-value or critical value method, but make sure to state which method you use.
A simple random sample of 80 adults is obtained, and each person’s red blood cell count is measured. The sample mean is 6.25 and a standard deviation of .65. Use a .01 significance level to test the claim that the sample is from a population with a mean less than 6.4, which is a value often used for the upper limit of the range of normal values. (For each hypothesis test state H0 and H1)
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVS equipped with tires made with compound 1 is 68 feet, with a population standard deviation of 13.9. The mean braking distance for SUVs equipped with tires made with compound 2 is 73 feet, with a population standard deviation of 13.7. Suppose that a sample of 72 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVS equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ, be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 1 of 5: State the null and alternative hypotheses for the test.
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 749 hours. A random sample of 28 light bulbs has a mean life of 720 hours. Assume the population is normally distributed and the population standard deviation is 64 hours. At α = 0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). (a) Identify the null hypothesis and alternative hypothesis. A. Ho: μ> 749 Ha: ≤749 (claim) D. Ho: μ≤ 720 Ha: μ>720 (claim) B. Ho: μ = 720 Ha: μ#720 (claim) E. Ho: μ#749(claim) Ha: μ = 749 O C. Ho: μ<720 (claim) Ha:μ ≥720 OF. Ho: μ ≥749 (claim) Ha: μ<749
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 65 feet, with a population standard deviation of 13.6. The mean braking distance for SUVs equipped with tires made with compound 2 is 69 feet, with a population standard deviation of 8.5. Suppose that a sample of 55 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ₁ be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 5 of 5: State the conclusion of the hypothesis test. Answer Tables Keypad Keyboard Shortcuts Previous Step Answers There is sufficient evidence…

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