Answer:
Correct options are (B) and (C).
Step-by-step explanation:
A two-sample <em>t</em>-test can be used to determine which of the two star financial planners, Brayden or Zoe, produced a higher mean rate of return last quarter for their clients.
The hypothesis is defined as:
<em>H₀</em>: The population mean rate of return for Brayden is same as that for Zoe, i.e. <em>μ</em>₁ - <em>μ</em>₂ = 0.
<em>Hₐ</em>: The population mean rate of return for Brayden is less than that for Zoe, i.e. <em>μ</em>₁ - <em>μ</em>₂ < 0.
The significance level of the test is, <em>α</em> = 0.05.
The decision rule is:
If the <em>p</em>-value of the test is less than the significance level of 5% then the null hypothesis is rejected.
And if the <em>p</em>-value of the test is more than the significance level of 5% then the null hypothesis is failed to be rejected.
The <em>p</em>-value of the test is computed to:
<em>p</em>-value > 0.10
If the <em>p</em>-value is greater than 0.10 then it is definitely greater than 0.05.
So, <em>p</em>-value > <em>α</em> = 0.05.
The null hypothesis will not be rejected at 5% level of significance.
<u>Conclusion</u>:
The conclusion of the hypothesis tests is that there is sufficient evidence to suggest that the population mean rate of return for Zoe is greater than the population mean rate of return for Brayden.
Thus, the correct options are (B) and (C).
