Use the AP Biology Statistics Manual for all formulas and definitions of variables. 

In the following problems, show your setup and work.

1. Graph the following sample data set showing the number of leaf disks that rise in a solution over time as photosynthesis occurs.
   
   
   
   
2. Calculate the mean and standard deviation for the data set of annual monthly rainfall. Use the data to sketch the appropriate graph.
   
   
   
   
3. A large ear of corn has a total of 377 grains, including 287 purple and 90 yellow.
   
   What is the hypothesized ratio of offspring from the parent generation?
   
   What is the chi square value and significance for the monohybrid cross?
   
   
4. A sample of 4 litters of rats from the same parents produced 29 black fur, black eyes; 8 black fur, red eyes; 10 white fur, black eyes; and 3 white fur, red eyes. 
   
   What is the hypothesized ratio of offspring? 
   
   What is the chi square value and its significance?

Try this Carolina kit:

Carolina Investigations® for AP® Biology: Quantitative Analysis and Statistics (item #747805A)

This kit uses genetics to teach and review the chi square test for fit of genetic crosses of corn, which reinforces Mendel's laws of inheritance. Students also practice identifying trends through past and present hominids using their own biometric measurements to calculate the mean, median, mode, and range of a sample. Samples are compared using a t-test. Students will also evaluate correlation of data sets using r-values.

Answers

1. Graph: Should be a line graph because the data is continuous with time on the x-axis and number of leafs disks on the y-axis.
   
   
   
   
2. Mean = 2.8 cm                 
   Standard Deviation = 1.9 cm             
   Graph: Must be a bar graph because data is categorical, with months on the x-axis and rainfall in cm on the y-axis.
   
   
   
   
3. A large ear of corn has a total of 377 grains, including 287 purple and 90 yellow.
   
   What is the hypothesized ratio of offspring from the parent generation?
   A 3:1 ratio of purple to yellow grains.
   
   What is the chi square value and significance for the monohybrid cross? 
   χ² = 0.26 with degrees of freedom = 1
   Therefore, the hypothesis is accepted, and the sample data fits the predicted ratio.
   
   
4. A sample of 4 litters of rats from the same parents produced 29 black fur, black eyes; 8 black fur, red eyes; 10 white fur, black eyes; and 3 white fur, red eyes. 
   
   What is the hypothesized ratio of offspring?
   9:3:3:1
   
   What is the chi square value and its significance?
   χ² = 0.28 with degrees of freedom = 3
   Therefore, the hypothesis is accepted, and the sample data fits the predicted ratio.

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