**Hypothesis Testing Tutorial**In this exercise, you are tasked with testing a statistical hypothesis at a significance level of 0.02.**Hypotheses:**- Null Hypothesis (\( H_0 \)): \( \mu = 78.6 \)- Alternative Hypothesis (\( H_1 \)): \( \mu < 78.6 \)You assume that the population is normally distributed, with a known standard deviation (\( \sigma \)) of 7.8. You have obtained a sample mean (\( \bar{x} \)) of 78 from a sample of size (\( n \)) of 50.**Part 1:**1. **Critical Value Calculation:** - Determine the critical value for this test. (Answer should be accurate to three decimal places.) - **Critical value = [Your answer here]**2. **Test Statistic Calculation:** - Calculate the test statistic for this sample. (Answer should be accurate to three decimal places.) - **Test statistic = [Your answer here]**

Note: As the direction of alternative hypothesis is "<", this is left-tailed test. The level of…

Answered: You wish to test the following claim…

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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You wish to test the following claim (Ha) at a significance level of a = 0.002. Ha:µ < 78.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 19 with mean = 70.4 and a standard deviation of s = 19.8. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. Oless than (or equal to) a Ogreater than a This p-value leads to a decision to. Oreject the null Oaccept the null Ofail to reject the nul As such, the final conclusion is that. OThere is sufficient evidence to warrant rejection of the claim tha: the population mean is less than 78.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 78.6. OThe sample data support the claim that the population mean is less than 78.6. OThere is not sufficient sample evidence to support the claim that the population mean is less than 78.6.
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately 80.3. You would like to be 95% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Use a critical value rounded to three decimal places.
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Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 6 samples is 4.6 pm with a standard deviation of 1.0 Does the data support the claim at the 0.05 level? Assume the population distribution is approximately normal. Step 4 of 5 : Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
You wish to test the following claim (H) at a significance level of a = 0.001. Ho:μ = 59.6 Ha: μ < 59.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 723 with mean M 59.2 and a standard deviation of SD = 5.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value The p-value is... o less than (or equal to) a Ogreater than a This test statistic leads to a decision to... o reject the null o accept the null o fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 59.6. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 59.6. The sample data support the claim that the population mean is less than…
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You wish to test the following claim at a significance level of a=0.10. H0:U=81.8 H1:U<81.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 90 with mean 77.6 and a standard deviation of 14.8.What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)This test statistic leads to a decision to reject the null accept the null fail to reject the null As such, the final conclusion is that there is sufficient evidence to conclude that the population mean is equal to 81.8. there is not sufficient evidence to conclude that the population mean is equal to 81.8. there is sufficient evidence to conclude that the population mean is less than 81.8. there is not sufficient evidence to conclude that the population mean is less than 81.8.

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