Question

A random sample of 18 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p- value and the critical and observed values of t for each of the following tests of hypotheses using, a = 0.01. Use the t distribution table to find a range for the p-value. Round your answers for the values of t to three decimal places. a. Ho:u= 46 versus H: 4 < 46. x X 36.94 47.86 < p-value tcritical -1.91 tobserved 2.898 b. Ho:u= 46 versus H:u * 46. X k p-value tcritical left tcritical right X tobserved

Answer 1

Given Data: á - H2H O8 n=18 001 ll -46 a) Ho: ll=46 If an-lz 18 -1 = 11 Hi : l<u6 tobserved -3.6 =x-ll olsa 42.446 8/ Vie :-1.909 tobserved -1.909 t critical = te= to,df 001, 11 -2567) (from t table) P-vake .. P[too <-1909) - P[tix 74909] using Excel = 7.DIST.RT (1.909, 17) From table 0.03 665 df = 17 t-1.909 between 10.025 <P < 0.05 0.025P-valo <0.05 b) Ho: b =46 Hi : 146. (2 tailed) Hobserved -71-909 tal, af +0.005,47 - +2.898 (from t table) tcritical t critical right = +2.998 t critical left = -2.898 P-vake for two tailed between 10.05 and at t= 1.909 df=17 0. 0.05 < Prake <0.1