2. A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kgwith a standard deviation of 0.5 kg. A sample of 50 lines will be used to test the hypothesis that u = 15 versus thealternative that u < 15. We will reject the null hypothesis if x < 14.9 . Find the probability of committing a Type 1Error.

Probability of Type I error is probability of rejecting the null hypothesis when it is actually…

Answered: 2. A manufacturer has developed a new…

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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The mean SAT score in mathematics,u, is 573. The standard deviation of these scores is 49. A special preparation course claims that its graduates will score higher, on average, than the mean score 573. A random sample of 33 students completed the course, and their mean SAT score in mathematics was 578. Assuming that the population is normally distributed. At the 0.1 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 49.
A social scientist suspects that the mean number of years of education for all adults in a large city is greater than 12 years. She will test her hypothesis using a random sample of 100 adults and finds the sample mean number of years is 12.98. Assume the standard deviation of the number of years of education for all adults is 3. State the appropriate null and alternative hypotheses.Find the value of the test statistic. Between what two p-values does your test statistic lie?
A random sample of 225 nails in a manufacturing company is gathered. The engineer specified length of a nail must be 8 centimeters having a standard deviation of 0.04 centimeters. It shows that the average weight of the nails is 8.055 centimeters. Do the produced nails exceed the specification of the engineer at a 1% level of significance. 1. What is the null hypothesis of the problem? 2. What is the alternative hypothesis of the problem and what is the direction of the alternative hypothesis?
It was reported that last year the average price of gallons of gasoline in a city X was $3.15. This year a sample of 50 gas stations had an average price of $3.10 for a gallon. We assume that the population standard deviation of prices is $0.15. We are interested in determining whether this year's mean price is less than last year. Perform a hypothesis test at the level of significance α=0.05.
A scientist has read that the mean birth weight u of babies born at full term is 7.3 pounds. The scientist, believing that the mean birth weight of babies born at full term is less than this value, plans to perform a statistical test. She selects a random sample of 75 birth weights of babies born at full term. Suppose that the population of birth weights of babies born at full term has a standard deviation of 1.8 pounds and that the scientist performs her hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) Н : μ is What are the null and alternative hypotheses that the scientist should use for the test? H, : u is Assuming that the actual value of u is 6.82 pounds, what is the power of the test? Round your response to at least two decimal places. What is the probability that the…
The mean SAT score in mathematics, u, is 545. The standard deviation of these scores is 39. A special preparation course claims that its graduates will score higher, on average, than the mean score 545. A random sample of 27 students completed the course, and their mean SAT score in mathematics was 566. Assume that the population is normally distributed. At the 0.01 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 39. Perform a one-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.)
BIG Corporation advertises that its light bulbs have a mean lifetime, µ, of at least 3000 hours. Suppose that we have reason to doubt this claim and decide to do statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample 2860 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, answer thi questions below. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test? H0 : µ is ____ ? _____ H1: µ is ____ ? ____ In the content of this test, what is a Type I error? A Type I error is ________ the hypothesis that µ is? _______ ?_______ when, in fact, µ is ? _______ Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ______
Suppose that a researcher is interested in estimating the mean systolic blood pressure, μ, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate u. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 25 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 6 mm Hg of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) 2 B M
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It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 50 healthy adults 1 to 4 times daily for 3 days, obtaining 225 measurements. The sample data resulted in a sample mean of 98.4°F and a sample standard deviation of 1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the oa = 0.01 level of significance. State the hypotheses. Ho: H = 98.6°F H1: H < 98.6°F Find the test statistic. tn = - 3.00 (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.)
The mean SAT score in mathematics is 587. The standard deviation of these scores is 42. A special preparation course claims that the mean SAT score, μ, of its graduates is greater than 587. An independent researcher tests this by taking a random sample of 100 students who completed the course; the mean SAT score in mathematics for the sample was 596. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 587? Assume that the population standard deviation of the scores of course graduates is also 42. Perform a one-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.) (a) State the null hypothesis H₁, and the alternative hypothesis H₁. H₁ :] H₁:0 (b) Determine the type of test statistic to use. t Degrees of freedom: (c) Find the value of the test statistic. (Round to…
A hat company states that the mean hat size for a male is at least 7.25. A random sample of 32 hat sizes has a mean of 7.15 and a standard deviation of 0.35. At α = 0.05, can you reject the company’s claim that the mean hat size for a male is at least 7.25? Be sure to state the p-value for this test. In the context of the problem, describe what a Type I error and a Type II error would mean. The mean ACT score for 43 male high school students is 21.1 and the standard deviation is 5.0. The mean ACT score for 56 female high school students is 20.9 and the standard deviation is 4.7. At the 1% significance level, can you reject the claim that male and female high school students have equal ACT score averages? Be sure to use the p-value to make your conclusion. A medical research team conducted a study to test the effect of a migraine drug. Of the 400 subjects who took the drug, 100 were pain free after two hours. Of the 407 subjects that took a placebo, 40 were pain free after two hours.…

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