5. A manufacturer claims that the mean tensile strength of thread A exceeds the averagetensile strength of thread B. To test his claim, 10 sample pieces of each type of thread aretested under similar conditions. Type A thread had a sample average tensile strength of 175kilograms with a standard deviation of 4 kilograms, while type B thread had a sample averagetensile strength of 165 kilograms with a standard of 5 kilograms. Assume that both populationsare normally distributed and the variances are equal. Use a=0.05.(a) Is there evidence to support the claim? Use critical region(s) for testing.(b) Calculate the P-value for the above test in part (a) and make a conclusion on the test.(c) Construct an appropriate 95% bound for the difference in mean tensile strength betweentype A and type B, that is µA – H; to test the hypothesis.(d) Test a claim that the mean tensile strength of type A thread would be at least 15 kilogramshigher than that of type B thread by using p-value.

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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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2) In the population, IQ scores are normally distributed with a mean of 100 and standard deviation of 15. We repeatedly pulled random samples of 50 individuals from the population and measured their IQ and the resulted mean was 92 with a standard deviation of 8. Test at a =0.05 significance if there is any statistically significant difference in the variance of the result. D. Focus DELL
An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis (at the 5% level of significance) that the variance of one of these yields is significantly larger than the other, what is the null and alternative hypotheses?
An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.0153 (fluid ounces) 2. If the variance of fill volume exceeds 0.01 (fluid ounces)2, an unacceptable proportion of bottles will be underfilled or overfilled. Using a level of significance of 0.05, and assuming that fill volume has a normal distribution, answer the following questions. If χ2critical = 30.14, is there evidence in the sample data to suggest that the manufacturer has a problem with underfilled or overfilled bottles?
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.6 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 1313 samples is 7.2 ppm with a variance of 0.49 Assume the population is normally distributed. A level of significance of 0.02 will be used. Make the decision to reject or fail to reject the null hypothesis.
5 c.)
A random sample of 10 subjects have weights with a standard deviation of 11.9848 kg . What is the variance of their weights ? Be sure to include the appropriate units with the result .
The mean age of 31 slot mechanic player is 51.3 years, and the standard deviation is 6.8 years.the mean age of a different sample of 35 roulette player is 54.8 year and standard deviation is 3.2 years. Can it be concluded at alpha = 0.01 that the mean age of slot machine players is less than those players roulette? Assume the variance are equal Step 1= Step 2= Step 3= Step 4=
2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a = 0.01.
One study claims that the variance in the resting heart rates of smokers is different than the variance in the resting heart rates of nonsmokers. A medical student decides to test this claim. The sample variance of resting heart rates, measured in beats per minute, for a random sample of 9 smokers is 480.7. The sample variance for a random sample of 9 nonsmokers is 131.6. Assume that both population distributions are approximately normal and test the study’s claim using a 0.10 level of significance. Does the evidence support the study’s claim? Let smokers be Population 1 and let nonsmokers be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0: σ21=σ22: Ha: σ21⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯σ22 Step 2 of 3: Compute the value of the test statistic. Round your answer to four decimal places. Step 3 of 3: Draw a conclusion and interpret the decision.
A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
The average size of a farm in Pekan I is 185 acres. The average size of a farm in Pekan II is 100 acre. Assume that the data were obtained from two samples with standard deviations of 38 acres and 12 acres, and sample size of 8 and 9 respectively. Can it be concluded at α = 0.05 that the average size of the farms in Pekan I and Pekan II are different? (Assume equal variances)
2. The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance. A. State the hypotheses. B. Determine the test statistic to use. C. Determine the level of significance, critical value, and the decision rule. D. Compute the value of the test statistic. E. Make a decision. F. Draw a conclusion.

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