### Hypothesis Testing: Choosing the Appropriate ProcedureWhen performing hypothesis testing to address specific research questions, selecting the correct testing procedure is crucial. Assume all samples are simple random samples, and use a significance level (α) of 0.05 if not specified.#### Scenario:A company is considering purchasing a new machine that is purportedly more efficient for producing ball bearings. Their decision hinges on whether the mean strength of bearings from the new machine is at least as strong as those from the old machine. The old machine produces ball bearings capable of withstanding 400 lbs per square inch.To test the new machine's performance:- The company tests 100 ball bearings from the new machine under standard operating conditions.- The average strength is found to be approximately 398.5 lbs per square inch.- The standard deviation (SD) is about 5 lbs per square inch.- The sample distribution appears non-normal.#### Question:Based on the above scenario, should the company purchase the new machine at α = 0.05?Which hypothesis testing procedure should be used?- One sample z-test for the population mean.- Two sample z-test for the population means.- One sample z-test for proportions.- Two sample z-test for proportions.- One sample t-test for the population mean.- None of our hypothesis tests fit.#### Explanation:The correct hypothesis test to use in this scenario is pertinent to several factors:1. We are comparing the mean strength of ball bearings from the new machine against the known mean strength of 400 lbs per square inch from the old machine.2. The sample size is 100 ball bearings.3. The distribution of sample data does not appear normal.4. The standard deviation is given.Given that the sample distribution does not follow a normal distribution and the sample size is relatively large, the appropriate test would generally be a **one-sample t-test for the population mean**; however, using a z-test could be considered if the sample size is sufficiently large for the Central Limit Theorem to apply, assuming normality of the sampling distribution.**Selected Procedure:**- **One sample t-test for the population mean.**To see the details of hypothesis testing procedures, you can refer to our statistics resource section.---In this educational context, the explanation provides a clear understanding of why a specific hypothesis test is selected, considering the data characteristics and scenario requirements.

The question is about to identify hypo. test Given : Popl. mean strength of bearings produced by old…

Answered: What hypothesis testing procedure…

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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Based on information from a previous study, r1 = 34 people out of a random sample of n1 = 105 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 = 105 adult Americans who did attend college, r2 = 50 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use ? = 0.01. (a) What is the level of significance?State the null and alternate hypotheses. H0: p1 = p2; H1: p1 ≠ p2H0: p1 < p2; H1: p1 = p2 H0: p1 = p2; H1: p1 < p2H0: p1 = p2; H1: p1 > p2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large.The Student's t. We assume the…
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Molly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80H0:p=0.80 versus Ha:p≠0.80Ha:p≠0.80 and calculates a test statistic of 1.10 with a pp-value of 0.273. Which of the following best represents the meaning of the pp-value? If the population proportion is 0.84, the probability of observing a sample proportion of 0.80 is 0.273. A If the population proportion is 0.84, the probability of observing a sample proportion of at least 0.04 less than 0.84 is 0.273. B If the population proportion is 0.80, the probability of observing a sample proportion within 0.04 of 0.80 is 0.273. C If the population proportion is 0.80, the probability of observing a sample proportion at least 0.04 greater than 0.80 is 0.273. D If the…
You hear on the local news that for the city of Kalamazoo, the proportion of people who support President Trump is 0.42. However, you think it is less than 0.42. The hypotheses you want to test are Null Hypothesis: p ≥ 0.42, Alternative Hypothesis: p < 0.42. You take a random sample around town and calculate a p-value for your hypothesis test of 0.7963. What is the appropriate conclusion? Conclude at the 5% level of significance. Question 4 options: 1) We did not find enough evidence to say the proportion of people who support President Trump is larger than 0.42. 2) We did not find enough evidence to say a significant difference exists between the proportion of people who support President Trump and 0.42 3) The proportion of people who support President Trump is significantly less than 0.42. 4) We did not find enough evidence to say the proportion of people who support…
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Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.
Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag and are Normally distributed with mean u. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised, so he intends to test the hypotheses Ho: μ = 14, Ha: μ < 14. To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the sample mean to be x = 13.88 and the sample standard deviation to be s = 0.24. Suppose in a similar test of 16 bags of these tortilla chips the P-value is 0.001. Further suppose that a is chosen to be 0.001. In that case, we would conclude that: Othere is not significant evidence that the mean net weight of the bags of chips is less than the advertised 14 oz. O there is not significant evidence that the mean net weight of the bags of chips is not less than the advertised 14 oz. O there is significant evidence that the…
What is the value of the sample test statistic? (Test the difference p₁ - P2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. 0-3 -2 -2 -1 -1 0 Read It 0 1 1 Watch it 2 2 3 0-3 ^ -1 0 1 -2 -2 -1 0 1 O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 2 2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. 3…
A December 2017 Gallup Poll reported that 43% of Americans use the internet for an hour or more each day. You suspect that a greater proportion of students at your school use the internet that much. You take a random sample of 60 students and find that 36 of them use the internet for an hour or more each day. Assume your school has more than 600 students. You will test the hypotheses H, : p = 0.43, H,:p>0.43 , where p= the true proportion of students at your school who use the internet for an hour or more each day. Which of the following gives the correct test statistic for this test? 0.43 - 0.6 Z = (0.6)(0.4) 60 0.43-0.6 (0.6)(0.4) 600 0.6-0.43 (0.6)(0.4) 60 0.6 - 0.43 (0.43)(0.57) 60 36 - 60 (36)(24) 60
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