Physicists have gathered at a conference where the results of an experiment exploring the value of a universal constant are to be revealed. Accepted wisdom suggests that the value of the universal constant should be Q = 0.13. After a drum roll, the results of n = 100 measurements of Q using a sensitive, expensive instrument are revealed to the crowd. A one-sample t-test with a significance threshold of = 0.005 is conducted testing the fol- lowing hypotheses:

H0 :Q=0.13 Ha :Q=0.13

The sample mean is revealed to be 0.1301, and the p-value of the test is revealed to be 0.0048. The conclusion of the test is that the null hypothesis should be rejected. The scientists in the audience gasp in disbelief.

(a) If the value of Q is actually 0.013 (i.e. if the null hypothesis is true), what is the probability that a test of this sort would produce a false positive finding? (This is a question about the process in general, not about this specific sample.)

(b) Determine the value of the t-statistic for this test using the information provided. (Hint: Keep in mind that this was a two-tailed test. You may use Geogebra for this task.)

c) A reporter in the audience approaches you and says: "Excuse me, but I'm not an expert and I don't really understand what is going on. Could you explain to me how a difference of 0.0001 could possibly be significant?" Provide an explanation to the reporter that reveals how you can determine the sample standard deviation from the information provided (reflecting the precision of the measurement instrument), and explain in general terms how this information is used in the hypothesis test to determine statistical significance.