Question

Problem 1 A student decided to perform at 5% sigfnificance level usual t-test for H:4=3 against H:4 3, for a sample of size n=10. But she did a mistake: used wrong degrees of freedom df - 10 instead of correct df - 11-1-9, so she used wrong critical value. What is the probability of type I error that she would have performing the test? Problem 2 Let X is amount of coffee in a "100g coffee can", EX = 4. With a sample of size 25 you test null of y=100 against > 100 at 5% significance level. Let X-Nu, oº) and variance is known: gol. (a) Find the decision rule for that test. (b) Suppose, actually y = 44, <100. What will be the probability to reject null of u = 100 in favor of the alternative u >100 in that case? Plot that probability as a function of a

Answer 1

1.

Critical Value for 5% significance (df = 10), tc = $\pm$ 2.228 (two-tailed)

but the df = 9, so the p-value corresponding to the above tc with df = 9 will be = 0.0529

i.e. Probability of type 1 error for the test actually becomes = 0.0529

Note: As per Chegg Policy, if multiple questions are uploaded together we need to answer the first question. I have solved Q1. Please upload the other question as a separate question.

Please upvote if you have liked my answer, would be of great help. Thank you.