a) A manufacturer has developed a new fishing line, which the companyclaims has mean breaking strength of 15 kilograms with a standarddeviation of 0.5 kilograms. To test the claim, a random sample of 50lines will be tested. The rejection region to be used is defined to bei< 14.9.i) State the mull and alternative hypotheses.ii) Find type I error probability, a.iii) Evaluate 3 for the alternative = 14.8.iv) Evaluate power function for the alternative u = 14.8.b) Suppose that we wish to test the hypothesis Ho : µ = 68 kg versusH1 : µ > 68 kg, for weights of male students at a certain college, usinga = 0.05 level of significance, when it is known that o = 5.i) Find the sample size required if the power of the test is to be 0.95when the true mean is 69 kg.ii) For what values of ī will the null hypothesis be rejected?

Answered: Image /qna-images/answer/e065cbfe-88df-40aa-ad12-83c7e614aebd.jpg

Answered: a) 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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In a sample of 27 blue M&Ms with a mean weight of 0.8560 g. Assume that population standard deviation is 0.0565g. Consider a hypothesis test that use a 0.05 significance level to test the claim that the mean weight of all M&Ms is equal to 0.8535 g. A) Find the null hypothesis and alternative hypothesis in symbolic form. B) Find the test statistics using the formula.
a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, x = 14.9 mm and a standard deviation, s = 1.33 mm. A test was %3D carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution. i. State, in symbols, the null and alternate hypotheses for this test. ii. State, with reasons, whether a t-test or a z-test will be appropriate. ii. (Determine the rejection region(s) of the test.
Suppose a university advertises that it's average class size is 37 or less. A students organization is concerned that budget cuts have led to increased class sizes and would like to test this claim. A random sample of 43 classes was selected, and the average class size was found to be 38.8 students. Assume that the standard deviation for class size at the college is 9 students. using a= 0.01, complete parts a and b below. a) does the student organization have enough evidence to refute the colleges claim? b) determine the p-value for this test.
The mean annual tuition and fees for a sample of 15 private colleges was 35,500 with a standard deviation of 6500. A dot plot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private collages is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value
7.) A sample of weights of 30 four-year-old boys had a standard deviaCon of 8.6 lbs. Can we claim that they have the same standard deviaCon as girls, which is 7.8 lbs? Test using ∝= 0.05 and a.) a hypothesis test b.) an appropriate confidence interval
A manufactures of personal music players has determined that the mean life of the players is 32.4 months, with a standard deviation of 6.3 months. a) What length of warranty should be offered if the manufacturer wants to restrict repairs to less than 1.5% of all the players sold? b) If 10 000 personal music players are sold, how many could the manufacturer expect to receive for repairs under warranty? c) The manufacturer wants to offer the option of purchases an extended warranty. If the manufacturer wants at least 80% of the players sold not to require repairs under extended warranty, what length of extended warranty should be offered?
A random sample of size 64 generated a sample mean of 80. The sample standard deviation is 16. a) Calculate the confidence interval (CI) for 95% confidence level (CL) for the population mean. b) What are the values of CI if CL changed to 90%?
a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, ?̅ = 14.9 mm and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution. State, in symbols, the null and alternate hypotheses for this test. ii. State, with reasons, whether a t-test or a z-test will be appropriate. iii. (Determine the rejection region(s) of the test. iv. Calculate the value of the test statistic. v. State, with reason, a valid conclusion for the test.
A bus company advertised a mean time of 150 minutes for a trip between two cities.A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 40 trips showed a mean x̄= 153 minutes and a standard deviation s=7.5 minutes.Set significance level at 10%. d) Verify conditions and calculate the value of the z-statistic? e) For what values of x̄ do we reject the null? f) Do we have sufficient evidence to say that the mean time is less than150 minutes? Explain.
A manufacturer makes ball bearings that are supposed to have a mean weight of 30g. A retailer suspects that the mean weight is actually less than 30g. The mean weight for a random sample of 16 ball bearings is 28.6g with a standard deviation of 4.4g. At the 0.05 significance level, test the claim that the sample comes from a population with a mean weight less than 30g. a)Identify the null hypothesis, alternative hypothesis. b)Find the test statistics c)Find the p-value d)Conclusion about the null hypothesis e)State the conclusion

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