Question

The 99 percent confidence interval for the average weight of a product is from 71.36 lbs. to 78.64 lbs. Can we conclude that μ is equal to 71, using a 99 percent confidence interval? Briefly explain.

Answer 1

Answer:

Step-by-step explanation:

Hello!

To decide over a hypothesis test using a confidence interval the following conditions are to be met:

1. The hypotheses should be two-tailed.

2. The hypotheses and the confidence interval should be made for the same parameter.

3. The confidence level and the significance level should be complementary, so if the CI is 1-α: 0.99 the level of significance should be α: 0.01

If all conditions are met, the decision rule is the following:

If the value stated in the null hypothesis is contained by the CI, the decision is to not reject the null hypothesis.

If the value stated in the null hypothesis is not contained by the CI, the decision is to reject the null hypothesis.

Let's say in this example the hypotheses are:

H₀: μ = 71

H₁: μ ≠ 71

α: 0.01

99% Confidence level is (71.36;78.64).

As you can see, 71 is not contained in the CI so the decision to take is to reject the null hypothesis, in other words, the population mean is not 71.

I hope it helps!