What's the best way to write a conclusion? (There are two equally good ways: find and select both.) [ ] The data provide strong evidence that students don't have equal preference for all class rows. In particular, they seem to prefer the Front somewhat. [ ] Observed counts differed from the counts the Null expected, but it's reasonable to ascribe the difference to chance variation in the sampling process. [ ] The data provide strong evidence that students don't have equal preference for all class rows. In particular, they seem to prefer the Middle somewhat. [ ] Observed counts differed so much from what the Null expected that it's not reasonable to ascribe the difference to chance variation in the sampling process. In particular, people seemed to prefer the Front more often than the Null expected.
Seating at GC
Thinking back again to the m111survey data frame, recall that the variable seat records where each subject prefers to sit in a classroom: Front, Middle, or Back.
Here is a table of the results:
gcSeat <- xtabs(~seat,data=m111survey)
gcSeat
## seat
## 1_front 2_middle 3_back
## 27 32 12
Now at Georgetown most classrooms are fairly small, with at about four rows actually in use:
- the first row is obviously the Front;
- most people would think of the second and third rows as the Middle;
- the fourth row would count as the Back.
If preferences for the four rows are exactly the same out there in the GC population, then one would expect that:
- 25% of the population prefers the Front;
- 50% prefer the middle (twice as many rows in the Middle, after all);
- 25% prefer the back.
We wonder if the available data provide strong evidence against the idea of equal preference among all four rows.
The results of the chi-sqaure test are as follows:
## Chi-squared test for given probabilities
##
## observed counts Expected by Null contribution to chisq statistic
## 1_front 27 17.75 4.82
## 2_middle 32 35.50 0.35
## 3_back 12 17.75 1.86
##
##
## Chi-Square Statistic = 7.028
## Degrees of Freedom of the table = 2
## P-Value = 0.0298
What's the best way to write a conclusion? (There are two equally good ways: find and select both.)
[ ] The data provide strong evidence that students don't have equal preference for all class rows. In particular, they seem to prefer the Front somewhat.
[ ] Observed counts differed from the counts the Null expected, but it's reasonable to ascribe the difference to chance variation in the sampling process.
[ ] The data provide strong evidence that students don't have equal preference for all class rows. In particular, they seem to prefer the Middle somewhat.
[ ] Observed counts differed so much from what the Null expected that it's not reasonable to ascribe the difference to chance variation in the sampling process. In particular, people seemed to prefer the Front more often than the Null expected.
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