Three classification categories were used perinatal stroke d

Three classification categories were used: perinatal stroke, delayed perinatal stroke, and childhood stroke. Of 59 children, 25 were diagnosed with delayed perinatal stroke. At the 5% level of significance, do the data provide sufficient evidence to conclude that delayed perinatal stroke does not comprise one-third of the cases among the three categories?

Name the appropriate test and calculate the test statistics and P-value

What is the conclusion?

Construct the appropriate 90% confidence interval

Solution

here sample size=n=59

let X be the random variable denoting the number children out of 59 children diagnosed with delayed perinatal stroke.

then X~Bin(59,p)

the hypothesis is

null hypothesis H₀: p=1/3    vs alternative hypothesis H₁:p not equal to 1/3

let f be the number of children out of 59 children diagnosed with delayed perinatal stroke

here f=25

then the test statistic is T=(f/n-1/3)/sqrt((1/3*2/3)/n) which under H0 asymptotically follows a N(0,1) distribution.

we reject the null hypothesi iff |t|>tao_alpha/2   where alpha=level of significance , t is the observed value of T and tao_alpha/2 is the upper alpha/2 point of a N(0,1) distribution

now n=59 f=25 alpha=0.05

|t|=1.4729  

now P value=2min{P[T<1.4729],P[1.4729]}=0.140778>0.05=level of significance

hence we accept H0 and conclude that delayed perinatal stroke does comprise one-third of the cases among the three categories.

90% confidence interval is

[f/n-sqrt((1/3*2/3)/n)*tao_0.05,f/n+sqrt((1/3*2/3)/n)*tao_0.05]

now tao_0.05=1.64 f=25 n=59

hence the confidence interval is [0.323,0.524] [answer]