**Hypothesis Testing for Mean Differences**In this exercise, you are required to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\).\[H_0: \mu_1 = \mu_2\]\[H_a: \mu_1 < \mu_2\]You obtain a sample size \(n_1 = 91\) with a mean of \(M_1 = 69.1\) and a standard deviation of \(SD_1 = 5.7\) from the first population. You obtain a sample size \(n_2 = 63\) with a mean of \(M_2 = 77.4\) and a standard deviation of \(SD_2 = 18.7\) from the second population.### Critical Value and Test Statistic Calculation**1. Critical Value**To determine the critical value for this test, use the conservative under-estimate for the degrees of freedom, as mentioned in your textbook. Report the answer accurate to three decimal places.\[\text{Critical value} = \_\_\_\_\_\_\]**2. Test Statistic**Calculate the test statistic for this sample and report the answer accurate to three decimal places.\[\text{Test statistic} = \_\_\_\_\_\_\]### Decision RuleThe test statistic is...- [ ] in the critical region- [ ] not in the critical region### ConclusionBased on the test statistic, make a decision to...- [ ] reject the null- [ ] accept the null- [ ] fail to reject the null### Final ConclusionThe final conclusion should be interpreted as follows:- [ ] There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.- [ ] There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.- [ ] The sample data support the claim that the first population mean is less than the second population mean.- [ ] There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.By completing the above steps, you will find out whether the hypothesis that the first population mean is less than the second population mean is supported by your sample data.

Name: **Hypothesis Testing for Mean Differences**In this exercise, you are
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: **Hypothesis Testing for Mean Differences**In this exercise, you are required to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\).\[H_0: \mu_1 = \mu_2\]\[H_a: \mu_1 < \mu_2\]You obtain a sample size \(n_1 = 91\) with a

Math

Statistics

You wish to test the following claim (H.) at a significance level of a = 0.10. T1 = In1:°H T1 > Irt : "H You obtain a sample of size n1 = 91 with a mean of M1 = 69.1 and a standard deviation of SD = 5.7 from the first population. You obtain a sample of size n2 = 63 with a mean of M2 = 77.4 and a standard deviation of SD2 = 18.7 from the second population. %3D What is the critical value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (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...

You wish to test the following claim (H.) at a significance level of a = 0.10. T1 = In1:°H T1 > Irt : "H You obtain a sample of size n1 = 91 with a mean of M1 = 69.1 and a standard deviation of SD = 5.7 from the first population. You obtain a sample of size n2 = 63 with a mean of M2 = 77.4 and a standard deviation of SD2 = 18.7 from the second population. %3D What is the critical value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (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...

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

To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
You wish to test the following claim (Ha) at a significance level of a = 0.10. H.: µ1 – µ2 = 0 Ha: µ1 – µ2 > 0 You obtain a sample of size nị the first population. You obtain a sample of size of s2 = 54.9 and a standard deviation of s1 = 78 with a mean of 2 65 with a mean of x1 17.1 from 46.7 and a standard deviation n2 7.2 from the second population. You will need to determine whether or not to pool so you will use the correct df. What is the critical value for this test? Report answer accurate to three decimal places. critical value
You wish to test the following claim (HaHa) at a significance level of 0.10. Ho:μ=80.1Ho:μ=80.1 Ha:μ<80.1Ha:μ<80.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=11n=11 with mean M=70.3M=70.3 and a standard deviation of SD=7.7SD=7.7. The test statistic is -4.221 What is the p-value for this sample?
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 Ho: Md = 0 versus Ha:μd 0 at a significance level of 0.10. For the context of this problem, d = μ₂ μ₁ where the first data set represents a pre-test and the second data set represents a post-test. You obtain pre-test and post-test samples for na 25 subjects. The average difference (post-pre) is d 7 with a standard deviation of the differences of sd = 11.6. = Round your answers to three decimal places, and round any interim calculations to four decimal places. What is the test statistic? =
You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=81.9 Ha:μ≠81.9You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12n=12 with mean M=72.6M=72.6 and a standard deviation of SD=7.5SD=7.5.What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = ______The p-value is... A.) less than (or equal to) αα B.) greater than α This p-value leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. C.) The sample data support the claim that the population mean is not equal to 81.9. D.) There is not sufficient sample evidence to…
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 14 samples is 4.9 ppm with a variance of 1.2 Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 2 of 5 : Find the value of the test statistic. Round your answer to three decimal places.
You wish to test the following claim (Ha) at a significance level of α=0.10. Ho:μ1=μ2 Ha:μ1<μ2 You obtain a sample of size n1=21 with a mean of M1=72.5 and a standard deviation of SD1=18.7 from the first population. You obtain a sample of size n2=22 with a mean of M2=76.2 and a standard deviation of SD2=15.8 from the second population. Use the Theory-based inference applet to conduct the test of significance. (a) What is the t-score for this sample? t-score = (Round to 2 decimal places.) (b) What is the p-value for this sample? p-value = (Round to 4 decimal places.) (c) The p-value is... less than (or equal to) α greater than α (d) This p-value leads to a decision to... strong evidence to support the alternative accept the null null is plausible (e) As such, the final conclusion is that... We conclude that μ1<μ2 . We conclude that μ1=μ2 . We have statistically significant evidence to support the claim that μ1<μ2 ..…
Question 7 > You wish to test the following claim (Ha) at a significance level of a = 0.05. H.: 41 Ha: µ1 7 42 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you have reason to believe that the variances of the two populations are equal. You obtain a sample of size nį = 14 with a mean of M1 first population. You obtain a sample of size n2 of SD2 = 7.4 from the second population. = 67.8 and a standard deviation of SD1 19 with a mean of M2 15.5 from the 61.7 and a standard deviation In the answer box below insert 2.0395 as 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 = %3D The test statistic is... O in the critical region O not in the critical region
You wish to test the following claim (H) at a significance level of a = 0.05. Ho: = 59.1 Ha:μ > 59.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 70 with mean M = 62.7 and a standard deviation of SD = 18.8. 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 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... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 59.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 59.1. The sample data support the claim that the population mean is greater than…