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# P1.T2.210. Hypothesis testing (Stock & Watson)

#### David Harper CFA FRM

##### David Harper CFA FRM
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AIMs: Explain and apply the process of hypothesis testing: Define and interpret the null hypothesis and the alternative hypothesis; Distinguish between one‐sided and two‐sided hypotheses; Describe the confidence interval approach to hypothesis testing; Describe the test of significance approach to hypothesis testing.

Questions:

210.1. Your colleague Robert wants to conduct a statistical test to determine whether hedge funds create alpha (i.e., excess return after attribution to all common factor exposure), on average. His test collects a large sample (n>30) and he is computing the mean (average) excess return such that the both the central limit theorem (CLT) and the law of large numbers apply. His null hypothesis is that, based on a sample of returns, the true (population) ex post realized alpha is approximately zero; therefore, the alternative hypothesis is that the true mean is non-zero and his two-tailed test allows for the possibility that funds destroy alpha via fees. He is going to test his hypothesis with a prespecified significance level of 5.0%, per convention. In this case, each of the following is true EXCEPT for:

a. He can conduct the test without computing a p-value
b. The probability of erroneously rejecting a true null hypothesis is 5.0%
c. He can reject the null if the t-statistic is greater than 1.96
d. If he reduces the significance level to 1.0%, he reduces the probability of erroneously rejecting a false null

210.2. Analyst Jane is concerned that the average days sales outstanding (DSO) in her coverage sector has increased above its historical average of 27.0 days (a lower number is better). From a large sample of 36 companies, she computes a sample mean DSO of 29.0 days with sample standard deviation of 7.0. Her one-sided alternative hypothesis is that DSO is greater than 27.0. Does she reject the null?

a. No, do not reject one-sided null as the t-statistic is less than 1.65
b. No, do not reject one-sided null as the t-statistic is less than 1.96
c. Yes, do reject one-sided null as the t-statistic is greater than 1.65
d. Yes, do reject one-sided null as the t-statistic is greater than 1.96

210.3. The average capital ratio of a sample of 49 banks is 7.4% with a sample standard deviation of 5.0%. What is the two-sided 95% confidence interval for the population's true average capital ratio; i.e., the random interval that has a 95% probability of containing the population mean?

a. 5.5% to 9.3%
b. 6.0% to 8.8%
c. 6.7% to 8.1%
d. 7.1% to 7.7%