Question

A scientist measured the speed of light. His values are in​ km/sec and have​ 299,000 subtracted from them. He reported the results of 22 trials with a mean of 756.22 and a standard deviation of 112.75.

​a) Find a 90​% confidence interval for the true speed of light from these statistics.

​b) State in words what this interval means. Keep in mind that the speed of light is a physical constant​ that, as far as we​ know, has a value that is true throughout the universe.

C)What assumptions must you make in order to use your​ method? Select all that apply.

A.The data come from a distribution that is nearly uniform.

B.The sample is drawn from a large population.

C.The measurements are independent.

D.The measurements arise from a random sample or suitably randomized experiment.

E.The data come from a distribution that is nearly normal.

Answer 1

solution =) Given clata n=22 D = 756,22 S=112.75 a C = 90). =0.go d=1-6 - 0:10 df-n- 22-1=21 to, olf = to 05, 21 = 1.721 goy confidence inderval for true speed: ă & topidl ts In = 756.22 + 1721 * 112.75 J22 756:22 £ 41.3701 (714.8499, 797,5901) T goy confidence interval (714.8499, 797.5901) 6 we are gol. confident that mean speed of light will lie under confidence interval (714.8499, 797.8901) Assumption the sample is drawn from a large population measurement are independent. ® The data come from a distribution that is nearly normal. © The