Question

(b) Referring back to (a), describe in context type I and II errors and say which error you might have made in reaching your conclusion. A type I error would be to fail to recognize that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. A type II error would be to incorrectly conclude that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. Since we failed to reject the null hypothesis in (a), we potentially committed a type II error. The source from which the data was obtained reported that ? = 1.33 for the population of all 762 such funds. So did you actually commit an error in reaching your conclusion? If we later find out that ? = , we have committed an error in reaching the conclusion. (c) Supposing that ? = 0.5, determine the power of the test in (a) for the actual value of ? stated in (b). Calculate the difference d and determine the power. (Round your answer for the power two decimal places.) d = power = Interpret the power of the test in (a) for the actual value of ? stated in (b) using the results from above. (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) This means that if the true values of ? and ? are ? = and ? = 0.5, then the probability of correctly rejecting the null hypothesis in favor of the alternate hypothesis at the 0.01 significance level is based upon a sample of size n = 20.

          (b) Referring back to (a), describe in context type I and II errors and say which error you might have made in reaching your conclusion.
A type I error would be to fail to recognize that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. A type II error would be to incorrectly conclude that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. Since we failed to reject the null hypothesis in (a), we potentially committed a type II error.
The source from which the data was obtained reported that ? = 1.33 for the population of all 762 such funds. So did you actually commit an error in reaching your conclusion?
If we later find out that ? = , we have committed an error in reaching the conclusion.
(c) Supposing that ? = 0.5, determine the power of the test in (a) for the actual value of ? stated in (b).
Calculate the difference d and determine the power. (Round your answer for the power two decimal places.)
d =
power =
Interpret the power of the test in (a) for the actual value of ? stated in (b) using the results from above. (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.)
This means that if the true values of ? and ? are ? = and ? = 0.5, then the probability of correctly rejecting the null hypothesis in favor of the alternate hypothesis at the 0.01 significance level is based upon a sample of size n = 20.

(b) Referring back to (a), describe in context type I and II errors and say which error you might have made in reaching your conclusion.
A type I error would be to fail to recognize that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. A type II error would be to incorrectly conclude that the population mean expense ratio for large-cap growth mutual funds exceeds 1% when the mean exceeds 1%. Since we failed to reject the null hypothesis in (a), we potentially committed a type II error.
The source from which the data was obtained reported that ? = 1.33 for the population of all 762 such funds. So did you actually commit an error in reaching your conclusion?
If we later find out that ? = , we have committed an error in reaching the conclusion.
(c) Supposing that ? = 0.5, determine the power of the test in (a) for the actual value of ? stated in (b).
Calculate the difference d and determine the power. (Round your answer for the power two decimal places.)
d =
power =
Interpret the power of the test in (a) for the actual value of ? stated in (b) using the results from above. (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.)
This means that if the true values of ? and ? are ? = and ? = 0.5, then the probability of correctly rejecting the null hypothesis in favor of the alternate hypothesis at the 0.01 significance level is based upon a sample of size n = 20.

Added by Kyle G.

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