Question

+ S do Холеро A local politician, running for reelection, claims that the mean prison time for car thieves is less mes louho than the required 5 years. A sample of 20 convicted car thieves was randomly selected, and the mean length of prison time was found to be 4 years and 6 months with a standard deviation of 1 year and 3 months. At the 0.05 level of significance, test the politician's claim Assume that the prison time for car thieves is normally distributed.

Answer 1

null hypothesis: HO: Alternate Hypothesis: Ha: 1.729 for 0.05 level with left tailed test and n-1= 19 degree of freedom, critical value of t= Decision rule: reject Ho if test statistic t<-1.729 population mean sample mean sample size sample std deviation 60 54.0000 20.00 15.000 standard error of mean = Sx=s/vn= 3.3541 t = (x-1)/sx= test statistic p value -1.789 0.0448

from above test statistic t =-1.789

as test statistic falls in rejection region, we reject null hypothesis and conclude that Politician claim is correct