Answer the following statement(s) true (T) or false (F)
Sixty-four independent measurements were made of the speed of light. They averaged 299,795 km/s and had a standard deviation of 8 km/s.
a. A 95% confidence interval for the speed of light is 299,795 ± 1.96 km/s.
b. The probability is 95% that the speed of light is in the interval 299,795 ± 1.96.
c. 95% of the measurements were in the interval 299, 795 ± 1.96.
d. If a 65th measurement is made, the probability is 95% that it would fall in the interval 299,795 ±1.96.
(a) True. This results from the expression , which is a 95% confidence interval.
(b) False. This is a specific interval, so it does not make sense to talk about the probability that it covers the true value.
(c) False. A confidence interval says something about where the true value is likely to be. It does not say anything about the proportion of the sample that is in the interval.
(d) False. A confidence interval says something about where the true value is likely to be. It does not say where the next measurement is likely to be.
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