University College Dublin

Considering the data provided in Question 4, the tile man- ufacturer would like to know if the tile length is longer than the benchmark value of 500 mm. Perform a hypothesis test for the population mean tile length with a level of significance of 0.05 and a level of precision of four decimal places. Answer the following questions: (a) What is the null hypothesis? [3 ] (b) What is the alternative hypothesis? [3 ] (c) What is the type of test (i. e., left-tailed/right-tailed/two-tailed)? [2 ] (d ) What is the value of the test statistic? Motivate your choice of distribution. [2 ] (e) Perform the hypothesis testing following the p-value approach: provide the [6 ] p-value and the rejection rule both mathematically and graphically. (f ) What is the outcome of the test (i. e., do you reject or not reject the null [4 ] hypothesis)? Provide an interpretation of the final result.

Yennefer is an old-school Dungeons and Dragons player. She rolls three fair six-sided dice to calculate her character’s strength stat. Let X be the total of the three numbers rolled. Find each of: (i ) the probability P (X = 18); [2 ] (ii ) the probability P (X = 17); [2 ] (iii ) the probability P (X = 15). [3 ] (b) Depressed by the low probability of getting the maximum of 18, Yennefer [7 ] decides to try a different method of rolling dice to find her strength stat. Namely, she will roll five fair six-sided dice and pick the three highest scores, then add these together to give her total strength. What is the probability that she will get 18 using this method? Show the details of your work. [Hint: think of rolling a six as success.] © UCD 2023 Page 3 of 6

Find the solution to the following recurrence: an=6an−1−8an−2+9n for n≥2 with initial conditions a0=13,a1=21 . an= ?

what are the benefits of toremifene for athletes. Please include Harvard style in text references after every point and at the bottom of the text with direct links

what are the benefits of toremifene for athletes. Please include Harvard style in text references after every point and at the bottom of the text

what are the benefits of toremifene for athletes. Please include in text references after every point