Please help me only if you really know how to solve it as I am stuck and I cannot solve these questions. Dont give me random answers please. You can use any software to solve it if it's easier ( we use R). If I am satisfied, i will also make sure you are satisfied too.

Link to textbook if needed with the content: https://drive.google.com/file/d/1ptM7Pzw8e364cZpwdQXU30GVhrQc1AZ7/view?usp=sharing

Questions:

Question Consider the following output for a one-sample procedure from R's t.test. One Sample t-test data: data t = 4.1894, df = 49, p-value = 0.0001162 alternative hypothesis: true mean is not equal to 15 95 percent confidence interval: 16.61141 19.58255 sample estimates: mean of x 18.09698 Which of the following statements are true? There may be more than one correct statement; check all that are true. [_] a) There is strong evidence that the true mean is greater than 15. Cl bl The p-value is double the area to the right of 4.1894 under a t distribution with 49 degrees of freedom. [_] c) One way to express the null hypothesis used in this test isHU : X = 15. l:' d) There must be an error in the output, since the sample mean should not lie within the confidence interval. Question : Suppose we are about to carry out 88 independent hypothesis tests. We intend to carry out each test at a significance level of 0.05. Suppose that the assumptions of each test are true, and, unknown to us, the null hypothesis is true in all 88 situations. What is the probability that we make a Type I error in exactly 10 of the 83 tests? (Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols.) Your Answer: . . Your