You wish to test the following claim (Ha): at a significance level of α=0.005 Ho: μ=64.3 Ha: μ≠64.3 You believe the population is normally distributed and you know the standard deviation is σ=19.4. You obtain a sample mean of x̄=68 for a sample of size n=69. What is the test statistic for this sample? Test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = Use Technology (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) α greater than α 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 not equal to 64.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 64.3. The sample data support the claim that the population mean is not equal to 64.3. There is not sufficient sample evidence to support the claim that the population mean is not equal to 64.3.
Added by Taylor W.
Step 1
Test for population mean: - Test statistic: t = (68 - 64.3) / (19.4 / sqrt(69)) = 3.747 (Note: we use t-distribution because the population standard deviation is unknown and we have a sample size greater than 30) - P-value: Using a t-table or calculator, we Show more…
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You wish to test the following claim (Ha) at a significance level of α=0.05. Ho: μ=52.8 Ha: μ≠52.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=55 with mean M=54 and a standard deviation of SD=6.7. 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) α greater than α 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 not equal to 52.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.8. The sample data support the claim that the population mean is not equal to 52.8. There is not sufficient sample evidence to support the claim that the population mean is not equal to 52.8.
Qudsiya A.
thoughtful Bird
Adi S.
Based on a simple random sample of 27 observations from a normal population, it was found that the average is 37. Assume that the population standard deviation is 9, and use a 9% significance level, to test the claim that the population mean is at least 42. 1. Read carefully the text and provide each of the following: 𝑛= 27 , 𝑥⎯⎯⎯= 37 , 𝜎= 9 , 𝛼= 9 %. 2. Express the claim and its opposite in symbolic forms. (Use "p" for the population proportion, "mu" for the population mean, "sigma" for the population standard deviation, and use whichever symbols you need of "<", ">", "< or=","> or=", "=", "not =", etc.) Claim: muor=42 Its opposite: mu<42 3. Identify the null hypothesis 𝐻0 and alternative hypothesis 𝐻0. (Use "p" for the population proportion, "mu" for the population mean, "sigma" for the population standard deviation, and use whichever symbols you need of "<", ">", "< or=","> or=", "=", "not =", etc. Write any proportion value as 0.12 instead of .12 or 12%) 𝐻0 : mu≥42 𝐻1 : mu<42 5. Is this hypothesis test two tailed, left tailed or right tailed. Choose the correct answer. A. left tailed test because of the less than sign in 𝐻1 B. left tailed test because of the greater or equal sign in 𝐻1 C. left tailed test because of the greater than sign in 𝐻0 D. right tailed test because of the not equal sign in 𝐻1 E. right tailed test because of the greater or equal sign in 𝐻0 F. left tailed test because of the less or equal sign in 𝐻0 G. two tailed test because of the not equal sign in 𝐻1 H. left tailed test because of the not equal sign in 𝐻1 6. Compare the claim and its opposite with the null and alternative hypotheses. A. The opposite of the claim and 𝐻0 are the same B. The claim and 𝐻1 are the same C. The claim and 𝐻0 are the same D. The opposite of the claim and 𝐻1 are the same. 6. The claimed value 𝜇= . 7. Compute 𝑥⎯⎯⎯⎯ − 𝜇𝜎𝑛√= (Round your answer to two decimal places). 8. The critical value is . (Round your answer to two decimal places). 9. The appropriate test statistic is (Round your answer to two decimal places). 10. The 𝑃-value is (Round your answer to four decimal places).
Sheryl E.
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