A cross of two heterozygous pea plants should give tall and dwarf offspring in the ratio 3 : 1…

Step 1. (a) Expected tall: $\tfrac{3}{4} \times 160 = 120$ plants. Expected dwarf: $\tfrac{1}{4} \times 160 = 40$ plants.

Step 2. (b) Tall: $\dfrac{(112 - 120)^2}{120} = \dfrac{64}{120} = 0.53$. Dwarf: $\dfrac{(48 - 40)^2}{40} = \dfrac{64}{40} = 1.60$. Chi-square $= 0.53 + 1.60 = 2.13$.

Step 3. (c) There are $2$ classes, so the degrees of freedom are $2 - 1 = 1$.

Step 4. The verdict. $2.13$ is less than $3.84$. The difference from $3 : 1$ is small enough to be chance, so the ratio fits.