AP Biology – Data Analysis and FRQ Practice

A student measures the length, in mm, of seven leaves from a plant: $23, 25, 21, 27, 24, 26, 22$.(a) Calculate the mean leaf length.(b) Calculate the sample standard deviation, correct to 3 significant figures.(c) Calculate the standard error of the mean (SEM), correct to 3 significant figures.

Explain why the standard error of the mean (SEM) is often a more useful statistic than the standard deviation when comparing the means of two different treatment groups in an experiment.

In an experiment investigating the effect of light intensity on the rate of photosynthesis in an aquatic plant, explain the difference between a control group and a controlled variable, giving one example of each for this experiment.

A researcher compares the mean height of two plant populations. Population A has a mean of $24\,\text{cm}$ with $\text{SEM} = 0.9\,\text{cm}$; Population B has a mean of $27\,\text{cm}$ with $\text{SEM} = 1.1\,\text{cm}$. Using $\text{mean} \pm 2\,\text{SEM}$ as an approximate 95\% confidence interval for each population mean, determine whether these data provide clear evidence that the two population means are different, and explain your reasoning.

A dihybrid genetic cross is predicted to produce offspring in a $9:3:3:1$ phenotypic ratio. Out of $556$ offspring observed, the counts for the four phenotype classes are $315$, $101$, $108$ and $32$.(a) Calculate the expected number of offspring for each phenotype class.(b) Calculate the chi-squared ($\chi^2$) statistic for these data.(c) The critical value of $\chi^2$ at $3$ degrees of freedom and $p = 0.05$ is $7.82$. State, with a reason, whether these data support the $9:3:3:1$ hypothesis.

State the null hypothesis being tested by the chi-squared test in the previous question, and explain what it means for the calculated $p$-value to be greater than $0.05$.

State two conditions that should ideally be met for an independent-samples t-test to be an appropriate statistical test for comparing two sample means.

A biologist hypothesises that increasing the concentration of a nitrogen-based fertiliser increases the growth rate of tomato plants.Design an experiment to test this hypothesis. In your answer, include:(a) the independent and dependent variables,(b) two variables that should be controlled, and why,(c) how a control group should be included,(d) how you would use the collected data (including an appropriate statistical test) to determine whether fertiliser concentration has a significant effect on growth rate.

A group of ecology students wants to compare species diversity between two woodland habitats. Explain how they should use random sampling and an appropriate sample size to obtain a reliable estimate of species diversity in each habitat, and describe one statistical test they could use to compare the two habitats’ diversity.

The activity of an enzyme was measured at a range of temperatures from $10\,^\circ\text{C}$ to $60\,^\circ\text{C}$. The rate of product formation increased steadily from $10\,^\circ\text{C}$ up to a maximum at $40\,^\circ\text{C}$, and then decreased sharply between $40\,^\circ\text{C}$ and $60\,^\circ\text{C}$.(a) Describe the relationship shown by these data.(b) Explain, in terms of enzyme structure, why the activity decreases sharply above the optimum temperature.