Question

] A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The following table shows the results when ten randomly selected cans are sampled. 11.77 11.85 11.87 11.96 12.03

12.03 12.09 12.18 12.28 12.36

(a) Compute the sample standard deviation (from the calculator).

(b) Perform a hypothesis test to determine whether the standard deviation is less than 0.2 ounce at the 5% significance level

Answer 1

a ) Given that, X 1.77 11.85 11.87 11.96 12-03 12.03 12.09 12.18 12:28 12-36 ori-sz²0.074 0.074 0.037 0.029 0.007 0.000 0.0001 0.002 0.01g 0.057 0101 n=10 Si=120.42 == {xi - 120.42 10 x = 12.042 Z(X; -50)? 0. = 0.3266 Sample Standard deviations s S = Eluci-5C)2 n-1 0.3266 107 s=oilgos b ) Null hypothesis'- Hoi 6=0.2 Hii 6 <012 Test statistics 2 xoa (n-1)s? 82 2 (10-1) (0.1905) (0.22 REDMI NOTE 6 PRO MI DUAL CAMERA Xo²8.1653

Oritical value q=oos d. f = n-1 =107 d-f=g xa, df = x005, g = 16.9189 .. Hence, x cal 2 <x crit Hence, we fail to reject to conclusion' - There is not sufficient evidence that the population standaod deviation is less than 0.2 ounce REDMI NOTE 6 PRO MI DUAL CAMERA