QUESTION 4(a) A manufacturing company claims that its workers have a mean productivity rate, per month, of atleast 40,000 per unit. The firm's human resources department randomly selected worker productivity datafor 50 months and claimed that the mean productivity figure to be 39200 per unit. The workersproductivity follows a normal distribution with a standard deviation of 14800 units.State the null and alternative hypotheses for this test.i.ii.iii.(b)(c)Find the p-value for the test of hypothesis.Will the null hypothesis be rejected at a 5% significance level?Using the statistics given above, construct a 95% confidence interval for the mean monthlyproduction figure for the company.The increase in salary demanded by a particular group of workers is normally distributed with amean of $ 81,000 and a variance of $790,000. If 30 workers were selected, what is the probabilitythat the mean salary increase request is at most $80,200.

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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

Consider a dataset containing the heights of 38 females who said they prefer to sit in the front of the classroom yields a sample average of 62 inches and a sample standard deviation of 2.5 inches. Suppose that the average height for the general population of college females is 65 inches. An analyst wants to test the claim that the true average height of females who prefer to sit in the front of the classroom is lower than it is for the general population. In the hypothesis for the above claim (at significance level of 10%), the appropriate test, test statistic (name and value), and pvalue is the approximate Z-test with z-statistic = 62 and pvalue = 0. the approximate Z-test with z-statistic = 7.40 and pvalue not calculable because normality is not given. = 0. the approximate Z-test with z-statistic = -7.40 and pvalue = 0.
The environmental research scientists report that the exhaust emissions for a certain car model has a normal distribution with a mean of 1.45 grams of nitrous oxide per mile and a standard deviation of 0.4. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A Simple random sample of 36 cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams. (a) State the null and alternative hypotheses. (b) Calculate the test statistic. (c) Calculate the Zc and p-value. Draw the picture. (d) What is the decision at the 0.05 significance level?
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.7. If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 4.4 lbs/square inch. Assume the standard deviation is known to be 0.9. If the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.
An electronics production sequence includes a process where a film of metal is deposited on a board. The film must be more than 1.000 mm thick. If the film is too thin the process fails. The engineer ran a test where the null hypothesis was that the mean thickness was at most 1.000 mm. A sample of 100 boards had a mean thickness of 1.007 mm and a standard deviation of 0.050 mm.At what level of significance would the null hypothesis be rejected? Express your answer at a decimal (not a percent) rounded to three places.
Suppose that Melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. What is the minimum number of babies should she sample if she wishes to be at least 90% confident that the mean birthweight of the sample is within 225 grams of the the mean birthweight of all babies? Assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g.

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