Chartered Financial Analyst Level 1

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Explanation:

When the population variances are unknown but assumed equal, the t-test for independent samples is calculated as:

$t = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$

where $S_p^2$ is the pooled variance estimator. Changing the hypothesized difference $(\mu_1 - \mu_2)$ directly affects the numerator of the test statistic, thereby altering its value.

Option B is incorrect because the degrees of freedom, calculated as $n_1 + n_2 - 2$ , remain unchanged regardless of the hypothesized difference.
Option C is incorrect because the pooled variance estimator $S_p^2$ is independent of the hypothesized difference in means.

Explanation:

When the population variances are unknown but assumed equal, the t-test for independent samples is calculated as:

$t = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$

where $S_p^2$ is the pooled variance estimator. Changing the hypothesized difference $(\mu_1 - \mu_2)$ directly affects the numerator of the test statistic, thereby altering its value.

Option B is incorrect because the degrees of freedom, calculated as $n_1 + n_2 - 2$ , remain unchanged regardless of the hypothesized difference.
Option C is incorrect because the pooled variance estimator $S_p^2$ is independent of the hypothesized difference in means.

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An analyst conducts a hypothesis test regarding the difference in mean returns between two portfolios, assuming normally distributed populations with unknown but equal variances. If the analyst adjusts the hypothesized difference in mean returns from 0% to 1%, which of the following will be affected?

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Last updated: February 22, 2026 at 14:03

The value of the test statistic.

75.0%

The degrees of freedom utilized in the test.

8.3%

The pooled estimate of the common population variance.

16.7%