Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 244thing is left to estimate, namely the value p=p 1 =P 2 . Once we specify a value of p, then,by the assumptions in the null hypothesis, all the p i are decided.We get the p-value in our example as follows:> y = c(35,40,25)> phat = c(75/200,75/200,25/100)> n = sum(y)> sum( (y−n*phat)^2/(n*phat))[1] 0.3333> pchisq(.3333, df =1 , lower.tail=FALSE)[1] 0.5637The difference is not statistically significant.In general, the χ 2 statistic can be used in significance tests where the null specifiessome relationship among the multinomial probabilities. The asymptotic distribution ofthe test statistic under the null hypothesis will be chi-squared. The degrees of freedomwill depend on the number of values that we are free to specify.9.1.3 Problems9.1 A die is rolled 100 times and yields the frequencies in Table 9.1. Is this a fair die?Answer using a significance test with H 0 :p i =1/6 for each i andTable 9.1 100 rolls of a dievalue1 2 3 4 5 6count 13 17 9 17 18 26H A :P i ≠1/6 for at least one i.9.2 Table 9.2 contains the results of a poll of 787 registered voters and the actual raceresults (in percentages of total votes) in the 2003 gubernatorial recall election inCalifornia.Table 9.2 California gubernatorial recall electionCandidate party poll amount actualSchwarzenegger Republican 315 48.6Bustamante Democrat 197 31.5McClintock Republican 141 12.5Camejo Green 39 2.8Huffington Independent 16 0.6other – 79 4.0a Source http://www.cnn.com/Is the sample data consistent with the actual results? Answer this using a test ofsignificance.