Question: Precision weighing devices are sensitive to environmental conditions. Temperature and humidity in a laboratory room where such a device is installed are tightly controlled to ensure high precision in weighing. A newly designed weighing device is claimed to be more robust against small variations of temperature and humidity. To verify such a claim, a laboratory tests the new device under four settings of temperature-humidity conditions. First, two levels of high and low temperature and two levels of high and low humidity are identified. Let T stand for temperature and H for humidity. The four experimental settings are defined and noted as (T, H): (high, high), (high, low), (low, high), and (low, low). A pre-calibrated standard weight of 1 kg was weighed by the new device four times in each setting. The results in terms of error (in micrograms mcg) are given below:
Test, using the ANOVA F-test at the 1% level of significance, whether the data provide sufficient evidence to conclude that the mean weight readings by the newly designed device vary among the four settings.