### Hypothesis Testing ExampleConsider the following hypothesis test:- Null Hypothesis ($H_0$): $\mu \leq 12$- Alternative Hypothesis ($H_a$): $\mu > 12$**Sample Information:**- Sample size ($n$): 25- Sample mean ($\bar{x}$): 14- Sample standard deviation ($s$): 4.32**Steps:****a. Compute the value of the test statistic (to 2 decimals).**[Value to be provided by the user]**b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.**- The p-value is: **between 0.005 and 0.01** (selected from a dropdown menu)**c. At $\alpha = 0.05$, what is your conclusion?**- Decision: **Reject null hypothesis** (selected from a dropdown menu)**d. What is the rejection rule using the critical value? (Use $\alpha = 0.05$.)**- Reject $H_0$ if $t$ is **less than or equal to** the critical value of [Value to be provided by the user] (to 3 decimals).**Conclusion:**- Can you conclude that the population mean is greater than 12? - **No** (selected from a dropdown menu)This example demonstrates hypothesis testing, utilizing a t-test to determine if there is significant evidence to support the claim that the population mean is greater than 12. The decision-making is based on the calculated p-value and critical values in relation to the significance level $\alpha$.

From the information, the hypotheses given are,Also, given thatThe claim is to test whether the…

Answered: Consider the following hypothesis test:…

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. H.:µ = 59.3 Ha:µ < 59.3 You believe the population is normally distributed and you know the standard deviation is o = 9.5. You obtain a sample mean of M = 58.3 for a sample of size n = 42. 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 e Type here to search HEWLETT-PA CKARD f3 14 esc f6 米 @ 2$ 4. 6. W E R. Y A|| S 3. 2.
Consider the following set of data. Sample Size Mean Standard Deviation Group 1 100 13,000 345 Group 2 80 12,850 500 Assume that the samples come from normal populations. Find the value of the test statistic used for testing the hypotheses Ho: 1 - 2 = 0 versus H - As 70. Ot = - 3.02 Ot = - 2.45 Ot = - 2.81 Ot = - 2.28 O None of the above.
A sample mean, sample standard deviation, and sample size are given. Perform the required hypothesis test about the mean, μ, of the normal population from which the sample was drawn. H0: μ ≤ 2.85, Ha: μ > 2.85, x = 3.26, s = 0.55, n = 9, α = 0.05
Perform the following hypothesis test: HO: µ = 10 H1: µ 10 The sample mean is 9.55, population standard deviation of 1.5 and a sample size of 51. Use a 5% significance level. What is the value of the test statistic? (Give your answer rounded to 2 decimals) (Be careful to make sure your + or - sign is correct)
Consider the following hypothesis test: Ho :µ = 17O Ha : µ + 170 A sample of 23 provided a sample mean of 182 and a sample standard deviation of 20. Find the value of the test statistic. Select one: O a. t= 0.60 O b. t = -0.60 O c. t= 2.88 O d. t=-2.88
The mean voltage and standard deviation of 10 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer Sample mean voltage (millivolts) Sample standard deviation (millivolts) A 136 3 B 132 5 What type of hypothesis test should be performed? What is the test statistic? What is the number of degrees of freedom? Does sufficient evidence exist to support the claim that the voltage of the batteries made by the two manufacturers is different at the α=0.1 significance level?
You wish to test the following claim (HaHa) at a significance level of α=0.001 Ho:μ=87.4 Ha:μ>87.4You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=82 with mean M=93.1 and a standard deviation of SD=12.5What 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) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null
Assume a significance level of α=0.1 and use the given information to complete parts (a) and (b) below. Original claim: The standard deviation of pulse rates of a certain group of adult males is more than 15 bpm. The hypothesis test results in a P-value of 0.2402. a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) Choose the correct answer below. A. Reject H0 because the P-value is greater than α. B. Fail to reject H0 because the P-value is greater than α. C. Reject H0 because the P-value is less than or equal to α. D. Fail to reject H0 because the P-value is less than or equal to α. b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A. The standard deviation of pulse rates of the group of adult males is less than or equal to 15 bpm. B. There is not sufficient evidence to support…
3. Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ>75; α=0.10 Sample statistics: x=76.4, s=2.9, n=24 a. The standardized test statistic is (Round to two decimal places as needed.) b. What is the P-value of the test statistic? P-value= (Round to three decimal places as needed.) c. Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. A. Fail to reject H0. There is not enough evidence to support the claim. B. Reject H0. There is enough evidence to support the claim. C. Fail to reject H0. There is enough evidence to support the claim. D. Reject H0. There is not enough evidence to support the claim.
Assume a significance level of α=0.01 and use the given information to complete parts (a) and (b) below. Original claim: The standard deviation of pulse rates of a certain group of adult males is more than 19bpm. The hypothesis test results in a P-value of 0.3876 A . State a conclusion about the null hypothesis. (Reject H0 or fail to rejectH0.) Choose the correct answer below. A. Reject H0 because the P-value is greater than α. B. Fail to reject H0 because the P-value is greater than α. C. Reject H0 because the P-value is less than or equal to α. D. Fail to reject H0 because the P-value is less than or equal to α b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A.There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 19 bpm. B. The standard deviation of pulse rates of the group of…

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