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# Hypothesis Testing of Sprinklers

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I need some help reviewing the sample problem below:
Sprinkler Systems. A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135 degrees F. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature between 133 degrees F with a standard deviation of 3.3 degrees F. At a level of significance of 0.10, do you have enough evidence to reject the manufacturers claim?

You need to do the following:
• Post the statement of this problem.
• Discuss the importance of obtaining a random sample.
• Identify the claim and state Ho and Ha.
• State the level of significance.
• Discuss the possibility of a Type I or Type II error.

On a separate page you need to do the following:
• Copy and paste the statement of the problem and your Ho and Ha from the previous page.
• Find the test statistic.
• Find the p-value.
• Decide whether to reject the null hypothesis.
• Interpret the decision in the context of the original claim.

##### Solution Summary

This solution consists of details of using one sample t-test to test the claim that the average activating temperature is at least 135 degrees F.

##### Solution Preview

Solution:
• Post the statement of this problem.
The average activating temperature is at least 135 degrees F.
• Discuss the importance of obtaining a random sample.
It is hard to get the whole population.
• Identify the claim and state Ho and Ha.
Ho: The average activating temperature is at least ...

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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