Question

Assume that the following confidence interval for the difference in the mean length of male​ (sample 1) and female babies​ (sample 2) at birth was constructed using independent simple random samples. What does the confidence interval suggest about the difference in length between male babies and female​ babies? minus0.2 in.less thanmu 1minusmu 2less than1.7 in. A. Male babies are longer. B. Female babies are longer. C. There is no difference in the length between male and female babies4

Answer 1

Answer:

$-0.2 \leq \mu_1 -\mu_2 \leq 1.7$

And we can see that the confidence interval for the true difference contains the value 0. So then we don't have enough evidence to conclude that the true means are significantly different at the confidence level selected $1-\alpha$ with $\alpha$ the significance.

So then based on this the best option for this case is:

C. There is no difference in the length between male and female babies

Step-by-step explanation:

For this case we have a sample 1 of males and a sample 2 of females and they construct a confidence interval for the true difference of population means for the length between male and female babies.

We need to remember that the formula for this true difference is given by this general expression:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

And for this case after construct the confidence interval they got the following result:

$-0.2 \leq \mu_1 -\mu_2 \leq 1.7$

And we can see that the confidence interval for the true difference contains the value 0. So then we don't have enough evidence to conclude that the true means are significantly different at the confidence level selected $1-\alpha$ with $\alpha$ the significance.

So then based on this the best option for this case is:

C. There is no difference in the length between male and female babies