Ascientist measured the speed of light. his values are in km/sec and have 299,000 subtracted from them. he reported the results of 25 trials with a mean of 756.22 and a standard deviation of 100.89.

(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?

a) The 90% confidence interval would be given by (721.716;790.724)  

b) We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)  

c) We assume the following conditions:

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Part a

represent the sample mean  

population mean (variable of interest)  

represent the sample standard deviation  

n=25 represent the sample size  

90% confidence interval  

The confidence interval for the mean is given by the following formula:  

(1)  

The degrees of freedom are given by:

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,24)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 90% confidence interval would be given by (721.716;790.724)  

Part b

We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)  

Part c

We assume the following conditions:

∞ this is your sign