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? minus −0.2 in. less than < mu 1 μ1 minus − mu 2 μ2 less than <1.7 in.a female babies are longer

b male babies are longer
c there is no difference in the length between male and female babies

Answer 1

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

Explanation:

Hello!

If I understood correctly, the interval [-0.2;1.7] was constructed to estimate the difference between the population mean of the length of male babies at birth(μ₁) and the population mean of the length of female babies at birth (μ₂).

Estimated parameter: μ₁-μ₂

To make a desition using an interval your hypothesis must be two-tailed,

H₀: μ₁-μ₂ = 0

H₁: μ₁-μ₂ ≠ 0

The level of significance should be complementary to the confidence level of the interval. (For example, if the interval was constructed at 1 - α: 0.9, the test should have a level of α: 0.10)

Remember the Confidence interval is an estimation of the real value of μ₁-μ₂, so, under the null hypothesis you can say that:

If the interval contains the 0, then you don't reject the null hypothesis.

If the interval doesn't contain the 0, you reject the null hypothesis.

So since 0 is contained in the confidence interval, you support the null hypothesis, in other words, there is enough information to say that there is no difference between the average length of male and female babies at birth.

I hope it helps!