Question

that fat guys are jolly. 9) The world's smallest mammal is the bumblebee bat (Craseonycteris thonglongyal). Such bats are roughly the size of a large bumblebee. Listed are weights (in grams) of a SRS of these bats: 1.7, 1.6, 1.5, 2.0, 2.3, 1.6, 1.6, 1.8, 1.5, 1.7, 2.2, 1.4, 1.6, 1.6, and 1.6. Assume the bats come from a population that is normally distributed. Use a 0.10 significance level to test the claim that these bats come from a population whose standard deviation is at most 0.20 grams. Horos 0.20 Ha: o > 0.20 bu Ho: d = 0.20 Ho: <0.20 Ha: 20.20 Hora 20.20 "Ha: <0.20 Ha: 0.20 10) See problem 9. State the critical value(s). a) 22.307 b) 7.790 c) 8.547 d) 21.064 11) See problem 9. Calculate the test statistic. a) 18.113 b) 8.364 C) 4.975 c) 4.975 d) 23.433 12) See problem 9. State the technical conclusion based on the traditional method. a) The test statistic is external to the critical value(s); Reject Ho. b) The test statistic is external to the critical value(s); FTR Ho. c) The test statistic is not external to the critical value(s); Reject Ho. d) The test statistic is not external to the critical value(s); FTR HO. 13) See problem 9. State the non-technical conclusion a) There is sufficient evidence to warrant rejection of the claim that these bats come from a population whose standard deviation is at most 0.20 grams. b) There is not sufficient evidence to warrant rejection of the claim that these bats come from a population whose standard deviation is at most 0.20 grams.

Answer 1

Claim : Standard deviation is at most 0.20 grams

9) H₀: σ ≤ 0.2    vs H_a: σ > 0.20

10) α = 0.10 , n = 15 , df = n-1 = 14

χ²_(0.1,14)   = 21.064 ---- from chi square distribution table.

11) First we need to find sample standard deviation (s) using excel function =STDEV.S()

A В D 1 1.7 2 1.6 -STDEV.S(A1:A15) 0.2588 3 1.5 4 2 5 2.3 6 1.6 7 1.6 8 1.8 9 1.5 10 1.7 11 2.2 12 1.4 13 1.6 14 1.6 15 1.6

Test statistic χ² =  $\frac{(n-1)*S^2}{\sigma ^2}$ = $\frac{14*0.2588^2}{0.2^2}$ = 23.433

12) As test statistic 23.433 is greater than critical value 21.064, We reject H₀

a) The test statistic is external to the critical value; Reject H₀

13) There is sufficient evidence to warrant rejection of the claim that these bats come from a population whose standard deviation is at most 0.20 grams.

14) a) It is probable the population standard deviation is greater than 0.20