Question

A random survey asked two samples of 100 high school students how much time they spend on homework each night. A 4-column table with 2 rows. Column 1 has entries Sample 1, Sample 2. Column 2 is labeled 0 to 30 minutes with entries 38, 41. Column 3 is labeled 31 to 60 minutes with entries 42, 36, Column 4 is labeled 61 to 90 minutes with entries 20, 23. Which inference is true? More students spend 0-30 minutes on homework than spend 31-60 minutes. More students spend 31-60 minutes on homework than spend 0-30 minutes. About the same number of students spend 0-30 minutes on homework as spend 31-60 minutes. More students spend 61-90 minutes on homework than spend 0-30 minutes.

Answer 1

The survey data indicates that about the same number of students in the combined samples spend 0-30 minutes on homework as spend 31-60 minutes.

Step-by-step explanation:

Comparing the given survey data for two samples of high school students, we can make some inferences about the time spent on homework. For both Sample 1 and Sample 2, more students report spending 0 to 30 minutes on homework than 61 to 90 minutes. However, when we compare the 0 to 30 minutes group to the 31 to 60 minutes group, Sample 1 has fewer students spending 0 to 30 minutes, while Sample 2 has more students in this time range.

For Sample 1, 38 students spend 0 to 30 minutes on homework, 42 students spend 31 to 60 minutes, and 20 students spend 61 to 90 minutes. For Sample 2, 41 students spend 0 to 30 minutes, 36 students spend 31 to 60 minutes, and 23 students spend 61 to 90 minutes.

Combining the data from both samples, 79 students spend 0 to 30 minutes on homework and 78 students spend 31 to 60 minutes. The inference closest to being correct is that about the same number of students spend 0-30 minutes on homework as spend 31-60 minutes, since the numbers are quite close when considering both samples together.

Answer 2

The correct inference from the given data is that about the same number of students spend 0-30 minutes on homework as spend 31-60 minutes, as the combined data from both samples show 79 and 78 students respectively in those time intervals.

Step-by-step explanation:

The question asks about an inference based on data collected from a survey on how much time high school students spend on homework each night. Given are two samples of 100 high school students with the distribution of time spent on homework broken into intervals: 0 to 30 minutes, 31 to 60 minutes, and 61 to 90 minutes.

From the first sample, there are 38 students who spend 0 to 30 minutes, 42 students who spend 31 to 60 minutes, and 20 students who spend 61 to 90 minutes on homework. In the second sample, there are 41 students who spend 0 to 30 minutes, 36 students who spend 31 to 60 minutes, and 23 students who spend 61 to 90 minutes on homework.

To make an inference, we combine the data from both samples:

0 to 30 minutes: 38 + 41 = 79 students

31 to 60 minutes: 42 + 36 = 78 students

61 to 90 minutes: 20 + 23 = 43 students

The inference that about the same number of students spend 0-30 minutes on homework as spend 31-60 minutes is true, based on the combined data from both samples.