4. Your financial advisor claims that the mean daily return of the S&P 500 is ze

Question

4. Your financial advisor claims that the mean daily return of the S&P 500 is zero. Is the actual mean a) Suppose that the true mean is 0.20. Then we certainly should reject our advisor's claim. But, this poer t.test(n-344,so-o.724, delta-.2, sig. level.es, type-one somple" nlerent than zero? To test, you use the same sample of n 244 daily retums from the previous problem. being statisties, we might not. The following is a power difference between the true mean and our advisor's claim.) calculation from R. (Note that "delta" is the One-sample t test power calculation 244 delta 2 sd . .774 sig. level - e.0s power e.9803169 alternative-two.sided Based on this output, what is the probability that we do not reject our advisor's claim? (Stated differently, what is the probability of a Type II Error?) b) Now suppose that the true mean is = 0.05. Again, we should reject our advisor's claim. The following is a power calculation from R. (Note that "delta" is the difference between the true mean and our advisor's claim.) power.t.test(n-244, sd-0.774, delta-.es, sig.level-.es, type-"one. sample") One-sample t test power calculation n 244 sd 0.774 power .1698212 delta e.e5 sig.level-e.0s alternative two, sided ased on this output, what is the probability that we do not reject our advisor's claim(Stated differently, what is the probability of a Type II Error?)

Explanation / Answer

answer:

we know,

The power of any test of statistical significance is defined as the probability that it will reject a false null hypothesis.

Statistical power is inversely related to beta or the probability of making a Type II error.

thus, In short, power = 1 – .

hence, If statistical power is high, the probability of making a Type II error, or concluding there is no effect when, in fact, there is one, goes down.

we will use this concept only in the above question,

4(a). we are given power = 0.9803169

thus , type II error = 1 - power = 1- 0.9803169 = 0.0196831( hence, low probability of making type II error)

4(b). we are given power = 0.1698212

thus , type II error = 1- power = 1- 0.1698212 = 0.8301788 (very high probability of making type II error)

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