### Hypothesis Testing with Unknown Population Standard Deviation#### Testing a Claim about a Population Mean (\(H_a\)) at a Significance Level of \(\alpha = 0.005\)Given Hypotheses:- Null Hypothesis: \(H_0: \mu = 71.5\)- Alternative Hypothesis: \(H_a: \mu > 71.5\)#### Sample Data- Sample size (\(n\)): 529- Sample mean (\(M\)): 72.9- Sample standard deviation (\(SD\)): 18.3### Critical Value CalculationTo find the critical value for this one-tailed test at a significance level of \(\alpha = 0.005\), one would typically refer to statistical tables or use statistical software.#### Test Statistic CalculationThe test statistic for the sample is calculated using the formula:\[ \text{Test statistic (t)} = \frac{M - \mu}{(SD/\sqrt{n})} \]Here:- \( \mu \) is the population mean under the null hypothesis.- \( M \) is the sample mean.- \( SD \) is the sample standard deviation.- \( n \) is the sample size.### Decision RuleDetermine the critical value and compare the test statistic to the critical region.- **The test statistic is...** - \( \square \) in the critical region - \( \squircle \) not in the critical regionBased on whether the test statistic falls within the critical region, proceed to make a decision.### ConclusionThe decision will lead to one of the following conclusions:- **This test statistic leads to a decision to...** - \( \bigcirc \) reject the null - \( \square \) accept the null - \( \squircle \) fail to reject the nullThen, make the final conclusion based on your decision:- **As such, the final conclusion is that…** - \( \bigcirc \) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. - \( \square \) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.5. - \( \squircle \) The sample data support the claim that the population mean is greater

Given information: The sample mean is M=72.9. The population mean is μ=71.5. The sample standard…

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 = 0.10. 51.3 Ηο:μ Ha:μ< 51.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 56 49.5 56.8 48.9 55.7 55.7 What is the test statistic for this sample? (Report answer accurate to 3 decimal places.) test statistic = What is the P-value for this sample? (Report answer accurate to 3 decimal places.) P-value =
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 wish to test the following claim (Ha) at a significance level of a = 0.005. H.: µ = 60.8 H.:u > 60.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 92.4 61.2 97.2 82.3 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... less than (or equal to) a O greater 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 greater than 60.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 60.8. The sample data support the claim that the population mean is greater than 60.8. There is…
You wish to test the following claim (HA) at a significance level of a = 0.002. H.:µ = 76.5 Ha: µ > 76.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 16 with mean M = 95.2 and a standard deviation of SD = 18.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = 4.1099 V What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =
You wish to test the following claim (Ha) at a significance level of a = 0.005.Ho: M = 59.3Ha: M > 59.3 You believe the population is normally distributed and you know the standard deviation is o = 18.1. Youobtain a sample mean of M = 68 for a sample of size n36. What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic =
The time to complete an exam is approximately Normal with a mean μ = 47 minutes and a standard deviation o = 8 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. 1. Fill in the indicated boxes. μ-3σ μ-2ο μίσ + μ μ+o 47 minutes. 2. Used the Empirical Rule to complete the following statements: 95% of testing times were between and μ = 47 σ = 8 μ+20 μ+30 minutes and 55 minutes. minutes % of the testing times were between 39
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You wish to test the following claim (H.) at a significance level of a = 0.005. H.:µ = 65.2 Ha:u < 65.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of 44.8 and a standard deviation size n 9 with mean M of SD = 14.2. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This p-value 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 warrant rejection of the claim that the population mean is less than 65.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. The sample data support the claim that the population mean is less than 65.2. There is not sufficient sample evidence to support the claim that the population mean is less than 65.2.
You wish to test the following claim (Ha) at a significance level of a = 0.05. H.:µ = 51.2 H.:µ + 51.2 You believe the population is normally distributed and you know the standard deviation is o = 19.9. You obtain a sample mean of M = 38.6 for a sample of size n = 24. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =
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.
These are the numbers I am working with: Sample mean= 78 Population mean= 75 Standard deviation:=10 Significance level: .05 Critical value: Z score > 1.96 Z score= 1.34 How do I figure the confidence limits for the 95% confidence interval. Z-score= 1.34 P-value= .1802
You wish to test the following claim (Ha) at a significance level of a = 0.02. H.:µ = 70.2 Ha:u < 70.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 53.5 57.6 58 61.3 58.3 70 76.5 71.4 44.6 70 66.8 80.6 What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - The test statistic is... O in the critical region O not in the critical region 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... O There is sufficient evidence to warrant rejection of the claim that the population mean is less than 70.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 70.2. O The sample data support the…

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