7) Consider the following null and alternative hypothesis.Ho : µ=120 versus H1: p> 120A random sample of 81 observations taken from this population produced a sample mean of123.5 and a sample standard deviation of 15. If this test is made at the 2.5% significance level, would youreject the null hypothesis?Solution:I.Statement of the Hypothesis:НоH1II.Statistical Test:III.Level of Significance and Critical Value:IV.Computed value of Z:V.Conclusion:

Answered: Image /qna-images/answer/c3a008f5-13ff-4742-8a4b-97c2501f4baf.jpg

Answered: 7) Consider the following null and…

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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A sample of 20 third-grade students had a average of 54 on a math proficiency test, with a sample standard deviation of 11. Is there enough evidence to conclude that the third-grade sample mean differs significantly from the third-grade population mean of 67? Assume a 0.02 significance level. Use the Critical Value Method of Testing (this means NO P-Values!). will need to have -1. The null hypothesis, Ho 2. The alternative hypothesis, H1 3. The test statistic4. The type of test(left, right, two-tailed) and the p-value 5. The decision to accept Ho or reject Ho
The Transportation Security Administration would like to compare the average amount of time it takes passengers to pass through airport security at Philadelphia versus Orlando during peak times. A random sample of 25 travelers in Philadelphia spent an average of 14.6 minutes to pass through airport security with a sample standard deviation of 5.8 minutes. A random sample of 27 travelers in Orlando spent an average of 11.5 minutes to pass through airport security with a sample standard deviation of 4.9 minutes. Perform a hypothesis test using α = 0.05 to determine if the average time to pass through security in Philadelphia is more than the average time to pass through security in Orlando. Assume the population variances for time through security at these two locations are equal. Hint: the alternative hypothesis should be μ1 - μ2 > 0.
If a sample of 40 individuals was taken from a population with a mean of 110 and a standard deviation of 10, what is the Z-score for a one-tailed hypothesis test at a significance level of 0.01 if the sample mean is 112?
An economist collects a simple random sample of 32 teacher's salaries in Cititon, and finds a mean of $67,000 and a standard deviation of $8,000. Is there enough evidence to conclude, at a significance of alpha= 0.05, that the mean salary of teachers in Cititon is different than $70,000? What is the test statistic? What is the null hypothesis? What conclusion do we draw? Do we reject the null hypothesis? What is/ are the critical value(s)? What is the alternative hypothesis? What is the p-value for the problem above?
Independent random samples of patients who had received knee and hip replacement were asked to assess the quality of service on a scale from 1 (low) to 7 (high). For a sample of 83 knee patients, the mean rating was 6.543 and the sample standard deviation was 0.649. For a sample of 54 hip patients, the mean rating was 6.733 and the sample standard deviation was 0.425. Test, against a two-sided alternative, the null hypothesis that the population mean ratings for these two types of patients are the same.
A lumber company is making boards that are 2781 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 14 boards is made, and it is found that they have a mean of 2784.3 millimeters with a standard deviation of 13. Is there evidence at the 0.05 level that the boards are too long and need to be trimmed? State the null and alternative hypotheses for the above scenario.
The human resources department of a large investment bank announced that the number of people it interviews monthly has a mean of 110 with a standard deviation of 15.5. The management of the bank suspects that the standard deviation exceeds 15.5. Suppose that the management wants to take a small sample of months and carry out a hypothesis test to see if its suspicions have support. State the null hypothesis H0 and the alternative hypothesis H1 that it would use for this test. Ho:___ H1:___
A manufacturer of kitchen water filters claims that their new model of water filter will, on average, treat more than 500 gallons of water before the water quality falls below acceptable levels. Consumer Reports wants to confirm this claim and selects a simple random sample of 60 filters for testing. Water was passed through each filter until the water quality dropped below acceptable levels and the volume of water measured. This produced a sample average of 575 gallons, and a sample standard deviation of 60 gallons. Construct a null and alternate hypothesis that Consumer Reports should use to confirm the manufacturer’s claim. Based on the sample data, what can they conclude? Use a 0.05 level of significance. Would your answer change if you used a 1% level of significance?
Sample surveys conducted in a large county in a cer-tain year and again 20 years later showed that originally the average height of 400 ten-year-old boys was 53.8inches with a standard deviation of 2.4 inches, whereas20 years later the average height of 500 ten-year-old boyswas 54.5 inches with a standard deviation of 2.5 inches.Use the four steps in the initial part of Section 1 andthe 0.05 level of significance to test the null hypothesisμ1 − μ2 = −0.5 against the alternative hypothesis μ1 −μ2 < −0.5.
A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (Department Store M minus Department Store V) ?
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.6 mg and a standard deviation of 3.25 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters? (a) What are the hypotheses? A. H0: μ = 21.1 mg H1: μ < 21.1 mg B. H0: μ = 21.1 mg H1: μ ≥ 21.1 mg C. H0: μ > 21.1 mg H1: μ < 21.1 mg D. H0: μ < 21.1 mg H1: μ ≥ 21.1 mg (b) Identify the P-value. (Round to four decimal places as needed.)…
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.4 mg and a standard deviation of 3.61 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters? a) What are the hypotheses? b) Identify the P-value. c) State the final conclusion. A. Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. B. Fail to reject H0. There is insufficient evidence to support…

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