Round figures to 2 decimal places. The tolerance for numeric answers is 0.01. Statistical tables are available at this link Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity, color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not smooth. For example, the difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the naked human eye, but the price of a 1 carat diamond tends to be much higher than the price of a 0.99 diamond. In this question, we use two random samples of diamonds, 0.99 carats and 1 carat, each sample of size n = 183, and compare the average prices of the diamonds. Some sample statistics are shown below. .77,'100 == 4136, .77,'0_99 = 49, In what follows, you are allowed to assume that the distribution of the point estimator is nearly normal, with standard error 1.51. Questions a. Which condition is essential for the sampling distribution of the point estimator to be nearly normal? O Independence of observations within samples and independence of samples O Independence of observations within samples but not independence of samples O Independence of samples but not independence of observations within samples O No conditions need to be satisfied b. Conduct a hypothesis test to evaluate if there is a difference between the average standardized prices of 0.99 and 1 carat diamonds. Test statistic: c. How large is the p-value of the test? O p>0.1 O 005

3.50, the probability is greater than or equal to 0.9998. *For Z