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Statistical hypothesis testing of temperature instruments

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A company compared the performance of two temperature instruments: one coupled to a process computer and the other used for visual control. Ideally, these two instruments should agree. The following data are the two temperatures over a five day period:

(see chart in attached file)

a. Conduct the most appropriate hypothesis test using a 0.05 significance level to determine if there is a statistically significant difference between the reading of both instruments,
b. Construct a 95% confidence interval for the true mean difference in temperature readings.

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This solution shows the steps in a hypothesis test and constructs a 95% confidence interval.

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A company compared the performance of two temperature instruments: one coupled to a process computer and the other used for visual control. Ideally, these two instruments should agree. The following data are the two temperatures over a five day period:

Day 1 2 3 4 5
Temp1 84.6 84.5 84.4 84.6 84.3
Temp 2 85.2 85.1 84.9 85.3 85.0
a. Conduct the most appropriate hypothesis test using a 0.05 ...

Solution provided by:
Changping Wang, MA
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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