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 trials with a mean of and a standard deviation of 30 trials with a mean of 756.22 and a standard deviation of 117.63.

a) Find a ​98% confidence interval for the true speed of light from these statistics.

b) 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?

​a) A ​98% confidence interval for the true speed of light is (_____________kn/sec.,___________km/sec)​(Round to two decimal places as​ needed.)

​b) In​ words, what does the ​98% confidence interval​ mean?

A. For all​ samples, ​98% of them will have a mean speed of light that falls within the confidence interval.

B. Any measurement of the speed of light will fall within this interval 98​% of the time.

C. With ​98% ​confidence, based on these​ data, the speed of light is between the lower and upper bounds of the confidence interval.

D. The confidence interval contains the true speed of light ​98% of the time.

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

A. The sample is drawn from a large population.

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

C. The data came from a distribution that is nearly uniform.

D. The measurements are independent.

E. The measurements arise from a random sample or suitabily randomized experiment.

Answer 1

Given :

Sample size = n = 30

Sample mean = = 756.22

Standard deviation = s =117.63

Significance level = = 1-0.98 = 0.02

Degree of freedom = df = n-1 = 30-1 = 29

At 0.02 significance level, the critical value of t is

b) It is given that

A scientist measured the speed of light. His values are in​ km/sec and have​ 299,000 subtracted from them.

Speed of light = 3×10^-8 m/s = 299792 Km/sec.

So 299792 - 299000 = 792

The confidence interval contains the true speed of light ​98% of the time.

The data come from a distribution that is nearly normal.