Answer the following statement(s) true (T) or false (F)
A metallurgist makes several measurements of the melting temperature of a certain alloy and computes a 95% confidence interval to be 2038 ±2°C.
a. There is 95% probability that the true melting temperature is in the interval 2038 ± 2°C.
b. If the experiment were repeated, the probability is 95% that the mean measurement from that experiment would be in the interval 2038 ± 2°C.
c. If the experiment were repeated, and a 95% confidence interval computed, there is 95% probability that the confidence interval would cover the true melting point.
d. If one more measurement were made, the probability is 95% that it would be in the interval 2038 ± 2°C.
(a) False. This a specific confidence interval that has already been computed. The notion of probability does not apply.
(b) False. The confidence interval specifies the location of the population mean. It does not specify the location of a sample mean.
(c) True. This says that the method used to compute a 95% confidence interval succeeds in covering the true mean 95% of the time.
(d) False. The confidence interval specifies the location of the population mean. It does not specify the location of a future measurement.
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