(Solved): In 1882 A. A. Michelson attempted to measure the speed of light-an important experiment in the hist ...

In 1882 A. A. Michelson attempted to measure the speed of light-an important experiment in the history of physics. The values given here are in \( \mathrm{km} / \mathrm{sec} \) and have had 299,000 subtracted from them. He reported the results of 23 trials with a mean of \( 756.218 \) and a standard deviation of \( 107.122 \) a) Find a \( 95 \% \) 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? a) A \( 95 \% \) confidence interval for the true speed of light is | \( \mathrm{km} / \mathrm{sec} \), \( \mathrm{km} / \mathrm{sec} \) ). (Round to two decimal places as needed.) b) In words, what does the \( 95 \% \) confidence interval mean? A. For all samples, \( 95 \% \) of them will have a mean speed of light that falls within the confidence interval. B. With \( 95 \% \) confidence, based on these data, the speed of light is between the lower and upper bourds of the confidence interval. C. The confidence interval contains the true speed of light \( 95 \% \) of the time. D. Any measurement of the speed of light will fall within this interval \( 95 \% \) of the time. c) What assumptions must you make in order to use your method? Select all that apply. A. The measurements arise from a random sample or suitably randomized experiment. B. The measurements are independent. C. The sample is drawn from a large population. D. The data follow a distribution that is nearly uniform. E. The data follow a distribution that is unimodal and reasonably symmetric.