Chi Squared Tests (Edexcel A Level Further Maths: Further Statistics 1): Exam Questions

Each day a gardener plants 4 seeds and records $X$, the number of the 4 seeds that germinate. The results for 100 days are shown in the table.

The gardener believes that $X$ can be modelled by the distribution $\text{B}(4,0.4)$.

A goodness-of-fit test is carried out to test this belief.

State the null hypothesis and the alternative hypothesis for this test.

One of the expected frequencies is less than 5.

(i) Show that the expected frequency for $X=4$ is 2.56

(ii) Hence state the number of degrees of freedom for the test.

The test statistic for this test is 1.15

Using a 5% level of significance, complete the test. You should state your critical value and conclusion clearly.