You want to compare the number of words per sentence in a sports magazine to the number of words per sentence in a political magazine.
a. The data represent random samples of 10 sentences in each magazine. Compare the samples using measures of center and variation. Can you use this to make a valid comparison about the magazines? Explain.
Sports magazine: 9, 21, 15, 14, 25, 26, 9, 19, 22, 30
Political magazine: 31, 22, 17, 5, 23, 15, 10, 20, 20, 17
a
The mean for the sports magazine is 19 and the mean for the political magazine is 18. However, the sample size is small to conclude that the number of words per sentence is about the same.
b
The mean for the sports magazine is 19 and the mean for the political magazine is 18. Because the samples are random, you can make a valid comparison that both magazines use about the same number of words per sentence.
c
The mean for the sports magazine is 20 and the mean for the political magazine is 18.5. However, the sample size is small to conclude that the number of words per sentence is about the same.
d
The mean for the sports magazine is 20 and the mean for the political magazine is 18.5. Because the samples are random, you can make a valid comparison that both magazines use about the same number of words per sentence.
b. The mean for the sports magazine is 19 and the mean for the political magazine is 18. Because the samples are random, you can make a valid comparison that both magazines use about the same number of words per sentence.
To compare the number of words per sentence in the sports magazine and the political magazine, we can use measures of center and variation. In this case, we can use the mean as the measure of center.
First, let's calculate the mean for each magazine:
Sports magazine: (9 + 21 + 15 + 14 + 25 + 26 + 9 + 19 + 22 + 30) / 10 = 19
Political magazine: (31 + 22 + 17 + 5 + 23 + 15 + 10 + 20 + 20 + 17) / 10 = 18
We can see that the means are very close: 19 for the sports magazine and 18 for the political magazine. This suggests that both magazines use a similar average number of words per sentence.
However, it's worth noting that the sample size is small (10 sentences) for each magazine. Therefore, it is important to consider the possibility of sampling variability, which means that the means might differ if we were to take a different set of sentences from each magazine.
In conclusion, based on the given samples and their means, we can make a valid comparison that both magazines use about the same number of words per sentence. However, it's important to acknowledge the limitations of the small sample size and the potential for sampling variability.