Pleases can you explain why we choose the answers. 7. You perform 1000 significa
ID: 3040581 • Letter: P
Question
Pleases can you explain why we choose the answers.
7. You perform 1000 significance tests using a significance level, a, of 0.05. Assume that all of the null hypotheses for the 1000 significance tests are true. How many of the 1000 significance tests would not result in a Type 1 error? A) 950 B) 50 C) 1000 D) 0 8. An engineer has designed an improved light bulb. The previous design had an average lifetime of 1200 hours. Using a sample of 2000 of these new bulbs, the average lifetime of this improved light bulb is found to be 1201 hours. Although the difference is quite small, the effect was statistically significant at the 0.05 level. Suppose that, in fact, there is no difference between the mean lifetimes of the previous design and the new design. Which of the following statements is TRUE? A) A Type I error has been committed. B) A Type II error has been committed. C) No error has been committed. 9. The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time,is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Assume that remains unchanged at 3 seconds. You decide to test the hypotheses H : -30 versus H: :30 at the 1% significance level. What is the range of x -values for which you will not reject Ho? A) (27.424, 32.576) B) (27.674, 32.326) C) (29.141, 30.859) D) (29.225, 30.775) : +24 using a level of A test was established off6: -24 against the alternative significance of a 0.05. The variable in question is known to be Normally distributed with -3. Hence, the null hypothesis would be rejected if a sample of size 16 has a mean 25.47. Suppose the distribution of the variable shifts to a new mean, -248, but the standard deviation does not change, what is the power of this test? A) 0.812 B) 0.95 C) 0.188 D) 0.858 E) 0.142 10.
Explanation / Answer
Answer to question# 7)
Total number of trials = 1000
significance level or type I error (alpha) = 0.05
The question tells us that the null hypothesis is true for all 1000 trials
Now type I error is that by mistake you end up rejecting the null , though in actual it was correct
thus : 0.05 times , we would end up rejecting the null , though ti is true
this imples the number of samples that we reject = 0.05 *1000 = 50
and the number of samples for which we do not conduct this type I error , and accpet the true null hypothesis will be equal to = 1000 -50 = 950
Thus the number of tests that would not result in Type I error = 950