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Answer: None of the above
For a two-sample t-test with equal variances assumed, the degrees of freedom is calculated as: **df = n₁ + n₂ - 2** Where: - n₁ = sample size for first quarter = 90 days - n₂ = sample size for second quarter = 90 days **Calculation:** df = 90 + 90 - 2 = 178 Since 178 degrees of freedom is not among the options A, B, or C, the correct answer is **D. None of the above**. **Key Points:** 1. When population variances are unknown but assumed equal, we use the pooled variance t-test. 2. The degrees of freedom for this test is n₁ + n₂ - 2. 3. The standard deviations provided (3% and 1.9%) are not used in calculating degrees of freedom for this test. 4. The significance level (5%) is also not relevant for determining degrees of freedom.
Author: Nikitesh Somanthe
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A researcher is trying to identify if the mean return on a specific asset in the first quarter of the year is different from its return in the second quarter of the year (quarter consisting of 90 days). He calculated the mean return for the first quarter as 16% with a standard deviation of 3%, and the return for the second quarter as 13.5% with a standard deviation of 1.9%. If the population variance is unknown but assumed to be equal, and the researcher intends to test at a 5% level of significance, how many degrees of freedom should he use?
A
181 degrees of freedom
B
180 degrees of freedom
C
179 degrees of freedom
D
None of the above