## E.11 Answers to Lecture 11 tutorial

### E.11.1 Answers to Sect. 11.1

1. Both students are incorrect as they used $$s$$ rather than $$\text{s.e.}(\bar{x})$$.
• Student A: This is an approximate 68% CI for the values of individual concrete samples, not for the mean, assuming the individual values have an approximate normal distribution.
• Student B: This is an approximate 95% CI for the values of individual concrete samples, not for the mean, assuming the first-crack strength are approximately normally distributed.
2. We need to use the standard error because the question asks about a sample mean… and standard errors tells us how much the sample means are likely to vary. $$12.4\pm(2\times 2.8\div\sqrt{6})$$, or $$12.4\pm 2.286$$ MPa, or from $$10.11$$ to $$14.69$$ MPa.

### E.11.2 Answers to Sect. 11.2

• RQ: Use mean distance. So more directly:

For casual golfers, is the mean distance travelled by a golf ball the same when hit by a wooden or metal club?

• Summaries: There is no mention of the distance travelled by the ball. It really doesn’t make sense to say ‘the iron golf club’ is ‘moderately higher than the wooden golf club’. That sounds like the height of the clubs are different!
• Results (1): Spelling/grammar errors (‘verse’; ‘differes’). Is two decimal places suitable? Certainly no more. The CI is for the difference between the means of hitting distances.
• Results (2): The results just say there is a difference between metal and wooden clubs (of course!); there is no mention of hitting distance.

### E.11.3 Answers to Sect. 11.3

• Null hypothesis: The mean heart rates.
• Results: A $$\chi^2$$ test is inappropriate for comparing means.

### E.11.4 Answers to Sect. 11.4

• RQ: Spelling error (‘lily pily’); mean size. It sounds odd, too, to ask if they ‘become’ longer. We are just comparing the mean length of leaves of eastern and western sides.

• Null hypothesis: Spelling again; and the hypothesis should be explicitly comparing the means: “For weeping lilly pilly trees at USC, it the mean leaf length the same for leaves on the western and eastern sides of the tree?”

• Results: Cannot find the mean of a qualitative variable (‘Side of tree’); the table should give the mean, standard deviation and standard error for leaves taken from the west side (one row) and the east side (second row), plus information about the difference.

• Methods: There are only five units of analysis. Leaves taken from the same tree are likely to share a lot in common: genetics; sunlight, watering regime, soil condition, etc. The students should have used 50 trees.

Alternatively, I suppose they could have used one tree (so the RQ was about what happens on one tree only), and compared 50 leaves on either side. While this is kinda OK, I do not recommend it.

### E.11.5 Answers to Sect. 11.5

• RQ: Cumbersome wording…; mean estimates.
• Null hypothesis: Spelling/grammar errors; mean again; where does ‘increased level of perception’ come from? We are just comparing estimation distances; perception is much more than just that.
• Results: This doesn’t answer the question. This is comparing the estimates from both groups—and yes, there may be a difference. But the RQ was about which group could estimate closer (on average) to the actual true width of the path. We still don’t know: The RQ was not answered.
• Discussion: You don’t prove anything like this… Again, what was tested doesn’t help answer the RQ.