Question

Previously, with a recent sample of 18 half carat diamonds, we determined a 99% confidence interval estimate of the mean price of all half carat diamonds to be ($1823.7, $2105.8).
a) In 2007 the mean price of a half carat diamonds was $2150. At the 1% significance level, does our recent sample of 18 half carat diamonds with the 99% confidence interval estimate provide evidence that the mean price has changed? Show (1) hypotheses, (5) decision based on C.I., and (6) the interpretation of the hypothesis test.

b) If we changed the significance level to 5%, can we still determine the decision of our hypothesis test? If so, what would the decision be? Provide reasoning.

Answer 1