6. Explain, in your own words, what it means for a result to be significant at t

Question

6. Explain, in your own words, what it means for a result to be significant at the.o5 level. 7. Are the following comments on significance testing correct or incorrect? Explain your answer- please write enough to show that you have a solid grasp of the relevant concepts and issues (a) The presentation of a result as x plus or minus signifies, in fact, that the true value [of what we are measuring has (about) 68% probability of lying between the limits x- and x + , and a 95% probability of lying between 2 and x-2 (b) Suppose you see a political poll reported in a newspaper, which says that Trudeau has an approval rating of 56% with a “margin of error" (corresponding to two standard deviations from the mean) of 3.5%. The newspaper describes the results of the poll as follows: it is

Explanation / Answer

6.

A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level, and is often denoted by . It simply means that if = .05, we are ready to allow type 1 error of 5 percent in our test.

The significance level, in the simplest of terms, is the threshold probability of incorrectly rejecting the null hypothesis when it is in fact true. This is also known as the type I error rate. The significance level or alpha is therefore associated with the overall confidence level of the test, meaning that the higher the value of alpha, the greater the confidence in the test.

The most common significance level is 0.05 (or 5%) which means that there is a 5% probability that the test will suffer a type I error by rejecting a true null hypothesis. This significance level conversely translates to a 95% level of confidence, meaning that over a series of hypothesis tests, 95% will not result in a type I error.

7. (Although I am answering, you should ask sperately)

a. When X follows normal distribution, or we take central limit theorem to be true (that is normal approximation is good. For 95%, it is around 1.96) then the statement is nearly Correct. (Under these assumptions only!)

b. Correct. As corresponding to 2 sigma band, the probability of the parameter outside the band should be 5%.

c.Incorrect

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