BIG Corporation advertises that its light bulbs have a mean lifetime, J, of 3000 hours. Suppose we have good reason to believe that u is less than 3000 hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2860 hours and that the sample standard deviation of the lifetimes is 650 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? X Ho : 1 H , :0 020 0=0 0#0 (b) Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? (Choose one) V X 5 ? (c) Suppose the true mean lifetime of BIG's light bulbs is 3000 hours. Fill in the blanks to describe a Type I error. A Type I error would be (Choose one) the hypothesis that u is (Choose one) (Choose one) V when, in fact, u is (Choose one)Ivanna rolled a number cube 150 times and got the following results. Outcome Rolled Number of Rolls Answer the following. Round your answers to the nearest thousandths. (a) From Ivanna's results, compute the experimental probability of rolling a 5 or 6. I] (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 5 or 6. I] (c) Assuming that the cube is fair, choose the statement below that is true. O The experimental and theoretical probabilities must always be equal. 0 As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. 0 As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart