Adrienne is comparing the daily high temperatures, in degrees Fahrenheit, in her city between 2018 and 2019. She selects 15 days from 2018 at random and 15days from 2019 at random and tracks the daily high temperature for each day. The results are provided in the table below.
Adrienne took 1,000 rerandomizations of the data and then subtracted the 2018 sample means from the 2019 sample means. She found that 42
had differences less than −14.5 degrees, 351
had differences less than −3.2 degrees, 378
had differences greater than 3.2 degrees, and 38
differences are greater than 14.5 degrees. Adrienne believes that the difference in the sample means is significant and that 2019 had cooler daily high temperatures compared to 2018. Explain whether Adrienne is correct
A) Adrienne is not correct because 3.8% of the samples had differences greater than 14.5 degrees, which is statistically significant. However, 2019 had warmer daily high temperatures compared to 2018.
B) Adrienne is not correct because 35.1% of the samples had differences less than −3.2 degrees, which is not statistically significant.
C)Adrienne is not correct because 37.8% of the samples had differences greater than 3.2 degrees, which is not statistically significant.
D) Adrienne is correct because only 4.2% of the samples had differences less than −14.5 degrees, which is statistically significant.