Question

Assume that the following confidence interval for the difference in the mean length of male babies​ (sample 1) and female babies​ (sample 2) at birth was constructed using independent simple random ​samples:0.2 in2.7 in. What does the confidence interval suggest about the difference in length between male babies and female​ babies?

Answer 1

Answer:

The confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.

Step-by-step explanation:

Consider the hypothesis for testing the difference in the mean length of male babies and female babies​ at birth:

H₀: There is no significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ ≠ 0.

The decision rule based on the confidence interval is:

If the (1 - α)% confidence interval does not consist of the null value, i.e. 0 then the null hypothesis will be rejected.

The confidence interval for the difference in the mean length of male babies and female babies​ at birth is:

CI = (0.2 in, 2.7 in)

The confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

Hence, concluding that there is a significant difference between the mean length of male babies and female babies​ at birth.

Since the confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.