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Ground or Air The earths temperature canbe measured using
Chapter 10, Problem 44(choose chapter or problem)
Ground or Air? The earths temperature canbe measured using either ground-based sensors orinfrared-sensing devices mounted in aircraft or spacesatellites. Ground-based sensoring is very accurate buttedious, while infrared-sensoring appears to introducea bias into the temperature readingsthat is, the averagetemperature reading may not be equal to the averageobtained by ground-based sensoring. To determinethe bias, readings were obtained at five different locationsusing both ground- and air-based temperaturesensors. The readings (in degrees Celsius) are listedhere:Location Ground Air1 46.9 47.32 45.4 48.13 36.3 37.94 31.0 32.75 24.7 26.2a. Do the data present sufficient evidence to indicate abias in the air-based temperature readings? Explain.b. Estimate the difference in mean temperaturesbetween ground- and air-based sensors using a 95%confidence interval.c. How many paired observations are required toestimate the difference between mean temperaturesfor ground- versus air-based sensors correctto within .2C, with probability approximatelyequal to .95?
Questions & Answers
QUESTION:
Ground or Air? The earths temperature canbe measured using either ground-based sensors orinfrared-sensing devices mounted in aircraft or spacesatellites. Ground-based sensoring is very accurate buttedious, while infrared-sensoring appears to introducea bias into the temperature readingsthat is, the averagetemperature reading may not be equal to the averageobtained by ground-based sensoring. To determinethe bias, readings were obtained at five different locationsusing both ground- and air-based temperaturesensors. The readings (in degrees Celsius) are listedhere:Location Ground Air1 46.9 47.32 45.4 48.13 36.3 37.94 31.0 32.75 24.7 26.2a. Do the data present sufficient evidence to indicate abias in the air-based temperature readings? Explain.b. Estimate the difference in mean temperaturesbetween ground- and air-based sensors using a 95%confidence interval.c. How many paired observations are required toestimate the difference between mean temperaturesfor ground- versus air-based sensors correctto within .2C, with probability approximatelyequal to .95?
ANSWER:Step 1 of 3
We conduct T-test for Paired Samples as:
Sample 1 |
Sample 2 |
Difference= Sample 1 - Sample 2 |
|
46.7 |
47.5 |
-0.8 |
|
45.5 |
48.2 |
-2.7 |
|
36.4 |
38.1 |
-1.7 |
|
31 |
32.8 |
-1.8 |
|
24.5 |
26.1 |
-1.6 |
|
Average |
36.82 |
38.54 |
-1.72 |
St. Dev. |
9.471 |
9.506 |
0.676 |
n |
5 |
5 |
5 |
From the sample data, it is found that the corresponding sample means are:
Also, the provided sample standard deviations are:
And the sample size is . For the score differences we have,