Part1:

Brunt et al. (2016) investigated various jumping characteristics of Kryptolebias marmoratus, an amphibious fish. The study compared jumping characteristics between a group of fish that had recently spent days out of water (Air), and a group of fish that spent days out of water but were then placed back in water for a recovery period (Recovery). There was also a control group in the experiment (that stayed in water the entire time), but we will ignore that group for the purposes of this question. Here we will compare the total distance travelled (cm) by the fish in their two jumping bouts (see the paper's experiment protocol section for full details). The data is contained in the data set s2050_F21_fishjump (see below), which can be found on the Courselink site. You must import this data set into R to carry out the analysis.

For your write-up to be complete, you must:

a) Plot side-by-side box plots of the data (in one plot). Label the plot appropriately.

b) Plot normal quantile-quantile plots for the two groups separately.

c) Make an argument in favour of using a two-sample t procedure on the raw data here, in spite of there being some question of the validity of the normality assumption.

d) Which two-sample t procedure would be more appropriate here? (i.e. Welch or pooled-variance?) Justify your choice.

e) Give the R output for your choice of procedure (Welch or pooled-variance t on the raw data).

f) Test the null hypothesis that the true mean total jumping distance is the same for both groups. Give appropriate hypotheses (in words and symbols), test statistic, p-value and conclusion.

g) Give an appropriate interpretation of the confidence interval given in the output. Your interpretation must relate to the problem at hand.

Part2:

a) Plot side-by-side box plots of the jump distances after applying a log transformation. (It doesn't really matter what base we use for the logarithm, but to make things a little simpler for the graders let's all go with natural logs (base e).) Label the plot appropriately.

b) Plot normal quantile-quantile plots of the log jump distances for the two groups separately.

c) Make an argument against using a two-sample t procedure on the raw data here (due to a violation of at least one assumption). What alternative method of analysis do you suggest?

For the remainder of this question, use an appropriate t procedure after applying a log transformation to the jump lengths. (Use natural logs, so we're all on the same page.) Carry this out in R.

d) Carry out a test of the null hypothesis that the true mean log distance is the same for both groups. Give appropriate hypotheses in words and symbols, value of the appropriate test statistic, p-value, and conclusion.

e) Give an appropriate interpretation of the 95% confidence interval from the R output, on the log scale. Your interpretation must relate to the problem at hand.

f) Back-transform the interval to give a 95% confidence interval on the original scale ofmeasurement.

g) Give an appropriate interpretation of this interval. Your interpretation must relate to the problem

at hand.

Data set:

Treatment Distance

Air 199.5

Air 99

Air 80.5

Air 67

Air 66.5

Air 45.5

Air 67

Air 37.5

Air 230.5

Air 112.5

Air 206

Air 27

Air 26

Air 201.5

Air 115

Air 74.5

Air 93.5

Air 290

Air 209

Air 143

Air 205.5

Air 31.5

Air 74.5

Air 162

Air 58.5

Air 363

Recovery 117.5

Recovery 34

Recovery 49

Recovery 62

Recovery 71.5

Recovery 7

Recovery 71.5

Recovery 25.5

Recovery 61.5

Recovery 131

Recovery 78

Recovery 14

Recovery 31

Recovery 44

Recovery 26.5

Recovery 31.5

Recovery 40.5