Anthony wants to know the average daily high temperatures in his town during the summer. He chose two random samples of 10 consecutive days and recorded the daily high temperatures. The daily high temperatures in Fahrenheit are as follows.
Sample 1: 78 82 85 87 90 85 79 86 91 88
Sample 2: 81 79 80 86 89 92 82 88 84 87
Find the mean daily high temperatures of each sample and calculate the difference between these mean daily high temperatures.
To find the mean daily high temperature of each sample, we need to add up all the temperatures and divide by the number of days (which is 10 in both samples).
Sample 1 mean: (78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88) / 10 = 85.1°F
Sample 2 mean: (81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87) / 10 = 84.8°F
To find the difference between these means, we simply subtract one from the other:
85.1°F - 84.8°F = 0.3°F
So the difference between the mean daily high temperatures of the two samples is 0.3°F.
To find the mean daily high temperature for each sample, you need to calculate the average of the values in each sample.
Sample 1:
Total of temperatures in Sample 1 = 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88
= 841
Mean daily high temperature for Sample 1 = Total / Number of values = 841 / 10 = 84.1°F
Sample 2:
Total of temperatures in Sample 2 = 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87
= 838
Mean daily high temperature for Sample 2 = Total / Number of values = 838 / 10 = 83.8°F
To calculate the difference between the mean daily high temperatures of Sample 1 and Sample 2, subtract the mean of Sample 2 from the mean of Sample 1.
Difference = Mean Sample 1 - Mean Sample 2 = 84.1 - 83.8 = 0.3°F
Therefore, the difference between the mean daily high temperatures of Sample 1 and Sample 2 is 0.3°F.