Researchers examined the bill color (in hue degree) of male and female zebra finches. Here are some summary statistics from the study: \[\begin{array} { | l | l | l | l | } \hline \text { Sex } & \boldsymbol { n } & \text { Mean } & \text { Standard Deviation } \\ \hline \text { Males } & 59 & 2.91 & 1.46 \\ \hline \text { Females } & 60 & 7.42 & 2.48 \\ \hline \end{array}\] We wish to address the question, How different are male and female zebra finches in bill color? What is the margin of error for a 95% confidence interval for the difference in mean bill color ?F-?M (in hue degree)?

A) 1.40 B) 1.02 C) 0.83 D) 0.74 A) 1.40 B) 1.02 C) 0.83 D) 0.74 D

The circumference of a species of tree was thought to be different depending on certain geographical factors. An SRS of 60 trees of this species is selected in Sequoyah National Forest, where it is found that x̄1= 6 meters with a standard deviation S1= 3 meters. A second SRS of size 40 trees of the same species is independently selected in Yellowstone National Forest, and it is found that x̄2= 4 meters with a standard deviation S2= 2 meters. Let μ1 and μ2 represent, respectively, the true mean circumferences of this species of tree. Assume the two-sample t procedures are safe to use. The researcher tests the following hypotheses: H0: μ1 = μ2 versus Ha: μ1 ≠ μ2 Which of the following statements is the correct interpretation for 99% confidence interval?

A) There is a 95% chance that the difference in population means is between 0.69 and 3.31 meters. B) There is a 95% chance that a randomly selected individual from this population would have a Response between 0.69 and 3.31 meters. C) We are 95% confident that the difference in sample means is between 0.69 and 3.31 Meters. D) We are 95% confident that the difference in population means is between 0.69 and 3.31 meters. A) There is a 95% chance that the difference in population means is between 0.69 and 3.31 meters. B) There is a 95% chance that a randomly selected individual from this population would have a Response between 0.69 and 3.31 meters. C) We are 95% confident that the difference in sample means is between 0.69 and 3.31 Meters. D) We are 95% confident that the difference in population means is between 0.69 and 3.31 meters.

Some chronic conditions produce episodes of severe flare-ups ("active" stage) between healthy periods ("inactive" stage). The active stage often necessitates immediate medical treatment. Researchers looked for biomarkers that might help identify these active stages. Here are data on the relative abundance of the protein BPG0235 in two independent random samples of men with the same chronic condition, 7 men in the active phase and 9 men in the inactive phase: \[\begin{array} { | l | l | } \hline \text { Active } & \text { Inactive } \\ \hline 1.0 & 1.1 \\ \hline 1.0 & 0.9 \\ \hline 1.0 & 0.5 \\ \hline 1.2 & 0.9 \\ \hline 1.2 & 1.0 \\ \hline 1.3 & 1.0 \\ \hline 1.0 & 0.8 \\ \hline & 0.7 \\ \hline & 1.1 \\ \hline \end{array}\] We want to know if there is a significant difference in the relative abundance of the protein BPG0235 between men in the active stage and men in the inactive phase. Therefore, we test the following hypotheses: ? H0: ?A= ?1 versus Ha: ?A? ?1 Which assumption must be true for the test results to be correct?

A) The population distributions must be roughly Normal. B) The sample standard deviations must be similar. C) The population standard deviations must be equal. D) The same individuals must be measured during an active phase and during an inactive phase. A) The population distributions must be roughly Normal. B) The sample standard deviations must be similar. C) The population standard deviations must be equal. D) The same individuals must be measured during an active phase and during an inactive phase.

Researchers examined the bill color (in hue degree) of male and female zebra finches. Here are the summary statistics from the study: \[\begin{array} { | l | l | l | l | } \hline \text { Sex } & \boldsymbol { n } & \text { Mean } & \text { Standard Error } \\ \hline \text { Males } & 59 & 2.91 & 0.19 \\ \hline \text { Females } & 60 & 7.42 & 0.32 \\ \hline \end{array}\] We are interested in testing the following hypotheses: H0: ?M=?F versus ?M??F What can we conclude from the 95% confidence interval for the difference in mean bill color ?F-?M (in hue degree)?

A) Reject the null hypothesis at significance level alpha 5% B) Fail to reject the null hypothesis at significance level alpha 5% C) Reject the alternative hypothesis at significance level alpha 5% D) Fail to reject the alternative hypothesis at significance level alpha 5% A) Reject the null hypothesis at significance level alpha 5% B) Fail to reject the null hypothesis at significance level alpha 5% C) Reject the alternative hypothesis at significance level alpha 5% D) Fail to reject the alternative hypothesis at significance level alpha 5%

The circumference of a species of tree was thought to be different depending on certain geographical factors. An SRS of 60 trees of this species is selected in Sequoyah National Forest, where it is found that x̄1= 6 meters with a standard deviation S1= 3 meters. A second SRS of size 40 trees of the same species is independently selected in Yellowstone National Forest, and it is found that x̄2= 4 meters with a standard deviation S2= 2 meters. Let μ1 and μ2 represent, respectively, the true mean circumferences of this species of tree. Assume the two-sample t procedures are safe to use. The researcher tests the following hypotheses: H0: μ1 = μ2 versus Ha: μ1 ≠ μ2 The 90% confidence interval is 2 ± 0.83 meters. What conclusion can we state based on this confidence interval?

A) We would reject the null hypothesis of no difference at the 0.10 level. B) The P-value is less than 0.10. C) Neither A nor B is correct. D) Both A and B are correct. A) We would reject the null hypothesis of no difference at the 0.10 level. B) The P-value is less than 0.10. C) Neither A nor B is correct. D) Both A and B are correct.