A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true...

 

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A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130°F. A sample of n=9 systems, when tested, yields a sample average activation temperature of 131.08°F. If the distribution of activation temperature is normal with standard deviation 1.5°F, you would like to know whether the test result contradict the manufacturer's claim at a significance level a = 0.01. Use this information and answer Question 1-15. Which of the following is the parameter of interest, µ? Which of the following is the null hypothesis? Which of the following is the alternative hypothesis test? Is this a one-sided or two-sided hypothesis test? What information in this scenario allows us to determine whether to use a Z-test or a t-test? Would you use a Z-test or a t-test? What is your critical value? (enter the negative critical value if it is a two-sided hypothesis test) What is the value of test statistic? Based on your test statistic and the critical value, what is the conclusion of this hypothesis test? What is the P-value? Based on the P-value, what is the conclusion of this hypothesis test? If the significance level is increased to 0.10, what would your conclusion of this hypothesis test based on the P-value that you calculated in Question 11? Assuming that reject region is either below 128.5°F or above 131.5°F, what is the probability that you would commit a type I error? Assume that the true average activation temperature is 133.5°F. What is the probability that you would commit a type II error with a significance level of 0.01? Assume that the true average activation temperature is 130.5°F. What would you expect the probability of committing a type II error would be when the same significance level is used as in Question 14? A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130°F. A sample of n=9 systems, when tested, yields a sample average activation temperature of 131.08°F. If the distribution of activation temperature is normal with standard deviation 1.5°F, you would like to know whether the test result contradict the manufacturer's claim at a significance level a = 0.01. Use this information and answer Question 1-15. Which of the following is the parameter of interest, µ? Which of the following is the null hypothesis? Which of the following is the alternative hypothesis test? Is this a one-sided or two-sided hypothesis test? What information in this scenario allows us to determine whether to use a Z-test or a t-test? Would you use a Z-test or a t-test? What is your critical value? (enter the negative critical value if it is a two-sided hypothesis test) What is the value of test statistic? Based on your test statistic and the critical value, what is the conclusion of this hypothesis test? What is the P-value? Based on the P-value, what is the conclusion of this hypothesis test? If the significance level is increased to 0.10, what would your conclusion of this hypothesis test based on the P-value that you calculated in Question 11? Assuming that reject region is either below 128.5°F or above 131.5°F, what is the probability that you would commit a type I error? Assume that the true average activation temperature is 133.5°F. What is the probability that you would commit a type II error with a significance level of 0.01? Assume that the true average activation temperature is 130.5°F. What would you expect the probability of committing a type II error would be when the same significance level is used as in Question 14?

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Solution It is given that the activation times is normal with standard deviation of 15 That is 15 Sa... View the full answer