Type I and Type II Errors in Investment Hypothesis Testing

Very Hard Hypothesis Testing Type I And Ii Errors

A financial analyst is conducting a hypothesis test to determine whether the average return of a new investment strategy is different from the market average of 8%. The null hypothesis ($H_0$) states that the average return of the new strategy is equal to 8% ($H_0: \\mu = 0.08$), while the alternative hypothesis ($H_a$) posits that the average return is not equal to 8% ($H_a: \\mu eq 0.08$). After performing the test, the analyst concludes that the average return is indeed significantly different from the market average and rejects the null hypothesis.

Assuming the null hypothesis is true, if the analyst erroneously rejects it and concludes the new strategy is better than the market average, this error is known as a Type I error. On the other hand, if the analyst fails to reject the null hypothesis when in fact the average return of the strategy is actually greater than 8%, this happens to be a Type II error.

Considering this context, which of the following statements correctly describes the implications of Type I and Type II errors in this scenario?

A Type I error indicates that the analyst promotes the new strategy as superior when it is not, leading to potential financial losses if investors follow this advice.

A Type II error implies the analyst misses the opportunity to recommend the new strategy, potentially resulting in gains missed by investors.

Both Type I and Type II errors suggest that the analyst should always reject the null hypothesis in favor of the alternative hypothesis to avoid mistakes.

Hint

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