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 Researchers wish to carry out a test of the null hypothesis that the mean of a certain population is 70 against a two-sided alternative hypothesis. In their situation, they (somehow) happen to know the population standard deviation. They feel comfortable assuming normality for this population, and carry out a 2 test. They draw a sample of 36 individuals from this population, and find a 2 test statistic of 0.35. What is the p-value of the test? (Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols.) Your Answer: a . Your Answer Question Researchers wished to investigate possible effects of an antivenom on swelling. 16 pigs were randomly assigned to an antivenom group or a control group [3 pigs to each group). All pigs were then subjected to a dose of snake venom, and either a dose of antivenom or a saline control. The researchers then measured the increase in leg volume (mL) after 8 hours as their measure of swelling. They carried out the pooled-variance t procedure in R, with the following results. Two Sample t-test data: antivenom_swelling and control_swelling t = 0.068927, df = 14, p-value = 0.946 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -94.11511 100.36511 sample estimates: mean of x mean of y 203.750 200.625 Of the following options, which one is the best conclusion to that hypothesis test? ("3, There is no evidence that the antivenom treatment and the control treatment ' have different sample mean swelling. ("'3 There is no evidence that the antivenom treatment and the control treatment J have different true mean swelling. (\""1 There is very strong evidence that the treatment and control have the same H effect on swelling. (\"3, There is very strong evidence that the antivenom treatment and the control \\. ' treatment result in exactly the same true mean swelling. 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