problem-9.7

problem-9.7  The first is done quite quickly using the defaults, as the uniform distribution is the null hypothesis.
> murder = c(53,42,51,45,36,36,65)
> chisq.test(murder)

        Chi-squared test for given probabilities

data:  murder
X-squared = 13.80, df = 6, p-value = 0.03189
  
The second we must do by hand. First note that if we specify pw, the weekend probability, then pd, the weekday probability, is (1-2pw)/5. There is only 1 degree of freedom. We estimate pw with the average of the weekend counts:
> n = sum(murder)
> phatw = (53 + 65)/(2*n)
> phatd = (1 - 2*phatw)/5
> e = n * c(phatw, rep(phatd,5), phatw)
> cs = sum ( (murder - e)^2/e )
> cs
[1] 5.077
> 1 - pchisq(cs,df=1)
[1] 0.02424

In both cases the p-value is small.