PROBLEM 1: (10 points) One university uses thousands of BrightLight fluorescent light bulbs each year. A new manufacturer, AmpleLamp, claims that its new brand of bulbs, which cost the same as the brand the university currently uses, has a mean life of 6000 hours. The university has never studied how long BrightLight bulbs last and they're curious to see how long BrightLight bulbs last compared to AmpleLamp bulbs. The university decides to conduct a significance test at the 0.05 significance level. Sixty-four BrightLight bulbs are tested and the mean life time is found to be 5910 hours. Both manufacturers report that the standard deviation for the lifespan of a light is 400 hours. Are the lifespans of the two brands of lights significantly different from each other? Mock Examination 2019 Dr. Ines Barkia a. What are the null and alternative hypotheses for this study? (2 pts) The null hypothesis is: The alternative hypothesis is: b. What is the type, mean, and standard deviation of the sampling distribution under the null hypothesis? (3 pts) c. What is the value of the sample mean, X? (1 pt) d. What is the standard z score and p-value for this test? (2 pts) e. Is the result statistically significant? What is the conclusion to this test of significance? Make sure to phrase your conclusion in terms of the scientific question of interest (saying that you reject or fail to reject the null hypothesis). (2 pts)