**Testing Population Mean with Unknown Standard Deviation**This page explains how to test a population mean when the standard deviation is unknown using the t-test. We will use the given data to determine the test statistic and the P-value, then make a decision regarding the null hypothesis.### Hypotheses and Significance LevelYou wish to test the following hypothesis at a significance level of α = 0.01:\[ H_0: \mu = 73.7 \]\[ H_a: \mu \neq 73.7 \]### Sample InformationThe population is assumed to be normally distributed, but the standard deviation is unknown. Your sample has the following characteristics:- **Sample size** (\(n\)): 54- **Sample mean** (\(\bar{M}\)): 65.8- **Sample standard deviation** (\(SD\)): 20.1### Test Statistic CalculationWhat is the test statistic for this sample? (Round the answer to 3 decimal places.)\[ \text{test statistic: } t = \_\_\_\_\_ \]### P-value CalculationWhat is the P-value for this sample? (Round the answer to 3 decimal places.)\[ \text{P-value: } \_\_\_\_\_ \]The P-value is:- ○ less than (or equal to) α- ○ greater than α### DecisionBased on the comparison between the P-value and α, decide:- ○ reject the null- ○ accept the null- ○ fail to reject the null### ConclusionSo, the final conclusion is:- ○ The data do **not** support the claim of the alternative hypothesis that the population mean is not equal to 73.7.- ○ The sample data **support** the claim of the alternative hypothesis that the population mean is not equal to 73.7.By completing the steps above, you will be able to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis, based on your sample data.

Name: **Testing Population Mean with Unknown Standard Deviation**This page
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: **Testing Population Mean with Unknown Standard Deviation**This page explains how to test a population mean when the standard deviation is unknown using the t-test. We will use the given data to determine the test statistic and the P-value, then mak

Introduction: Denote μ as the true population mean.

Math

Statistics

You wish to test the following claim (Ha) at a significance level of a = 0.01. H.:µ = 73.7 Ha:µ + 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 54 mean: M = 65.8 standard deviation: SD = 20.1. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) a greater than a This leads to a decision to... O reject the null accept the null O fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is not equal to 73.7. O The sample data support the claim of the alternative hypothesis that the population mean is not equal to 73.7.

You wish to test the following claim (Ha) at a significance level of a = 0.01. H.:µ = 73.7 Ha:µ + 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 54 mean: M = 65.8 standard deviation: SD = 20.1. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) a greater than a This leads to a decision to... O reject the null accept the null O fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is not equal to 73.7. O The sample data support the claim of the alternative hypothesis that the population mean is not equal to 73.7.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

You wish to test the following claim (H) at a significance level of a = 0.05. H.:µ = 65.2 Ha:µ < 65.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 571 with mean M = 63.2 and a standard deviation of SD = 20.3. 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. reject the null accept the null 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 65.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. O The sample data 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 = 0.01. H.: µ = 62.4 Ha:H > 62.4 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 31 with mean M 63.6 and a standard deviation of SD = 10.9. 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 =
Consider the following data: x 4 5 6 7 8 P(X = x) 0.2 0.2 0.1 0.2 0.3 Step 3 of 5: Find the standard deviation. Round your answer to one decimal place. Copy Data
Please help me to explain this questions in steps. Thank you.
i need help solving this homework question: the lengths of nails (in millimeters) at a certain plant are normally distributed with a mean of 20.00 and a standard deviation of 0.21. nails produced will be rejected unless their lengths are between 19.71 mm and 20.42 mm. what percent of the nails are accepted?
You wish to test the following claim (H) at a significance level of a = 0.01. Ho:μ = 87.4 Ha:μ< 87.4 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 M = 85.3 and a standard deviation of SD = 15.6. 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 p-value leads to a decision to... O reject the null accept the null O fail to reject the null
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…
In a particular statistics exam, the 35th percentile of final exam score is 42, and the 70th percentile of final exam score is 76. A histogram of the scores approximately follows the normal curve. What is the approximate standard deviation of the final exam scores? Hints: What is the z value in the normal table that gives you closest to 35% of the area between -z and z? Now what does that tell you about the number of SDs in between 42 inches and 76 inches? You might find it helpful to draw a picture of the normal curve with original units and standard units. Group of answer choices a. 7.5 b. 13.1 c. 20.7 d. 37.8
You wish to test the following claim (H.) at a significance level of a = 0.01. H.:µ = 75.8 Ha:µ > 75.8 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 73 mean: M = 77.2 standard deviation: SD = 8.5. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P.value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... O less than (or equal to) a O greater than a This leads to a decision to... O reject the null O accept the null O fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is greater than 75.8. O The sample data support the claim of the alternative hypothesis that the population mean is greater than 75.8.
You wish to test the following claim (H.) at a significance level of a = 0.02. H.:µ = 71.8 Ha:u > 71.8 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 I = 89.2 and a standard deviation of s = 17.6. 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 O greater than a This p-value leads to a decision to... O reject the null O accept the null O do not 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 greater than 71.8. O There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.8. O The sample data support the claim that the population mean is greater than 71.8. O There is not sufficient sample evidence to súpport the claim that the population mean is greater…
You wish to test the following claim (H.) at a significance level of a 0.02. H,:p = 79.3 H: u > 79.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 7 with mean M 105.5 and a standard deviation of SD= l6.5. %3D 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 greater than a This p-value leads to a decision to... reject the null Oaccept the null fail to reject the null As such, the final conclusion is that... 5There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 79.3. | There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 79.3. The sample data support the claim that the population mean is greater than 79.3. There is not sufficient sample evidence to support the claim that the population mean is greater than 79.3.
You wish to test the following claim (H) at a significance level of a = 0.10. H.:µ = 66.2 Ha:µ + 66.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 10 with mean M = 43.4 and a standard deviation of SD = 18.5. 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 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. O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 66.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 66.2. O The sample data support the claim that the population mean is not…