Phenytoin is a standard anticonvulsant drug that unfortunately has many toxic side effects. A study was undertaken to compare phenytoin with valproate, another drug in the treatment of epilepsy. Patients were randomly allocated to receive either phenytoin or valproate for 12 months. Of 20 patients receiving valproate, 6 were free of seizures for the 12 months, while 6 of 17 patients receiving phenytoin were seizure free.
(a) Consider a chi-square test to compare the seizure-free response rates for the two drugs using a non directional alternative.
(i) State the null and alternative hypotheses in symbols.
(ii) What is the value of the test statistic?
(iii) The P-value for the test is 0.73. If α = 0.10, what is your conclusion regarding the hypotheses in (ii)?
(b) Do your conclusions in part (a)(iii) provide evidence that valproate and phenytoin are equally effective in preventing seizures? Discuss.