Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X)....

Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations
x = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120
y = 0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67.95, 72.11, 76.02, 80.01, 84.10, 88.06, 91.74, 96.02, 99.95, 103.87, 108.01, 111.99, 116.04, 120.03
We want to test if these thermometers seem to be measuring the same temperatures. Let's use the threshold . Answer all questions up to 3 decimals

(a) Write down the appropriate hypothesis tests for . H₀:   ---Select--- ≠ = > <  and H_a:   ---Select--- ≤ = > ≠ ≥ <

(b) The test statistic is  (Use 2 decimal places)

(c) The p-value is  (Use 4 decimal places)

(d) Therefore, we can conclude that

The data provides evidence at the 0.1 significance level that these thermometers are not consistentThe data provides no evidence at the 0.1 significance level that these thermometers are not consistentThe probability that the null hypothesis is true is equal to the p-valueThe probability that we have made a mistake is equal to 0.1

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orchestra answered 2 years ago

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