Question

A researcher reports the following confidence interval for a comparison of the difference between two groups: 95% CI −12.0 [−30.0 to 6.0].
If there was no difference between groups, then a difference of 0 was expected. 1.

What would the decision have likely been if the researcher tested this hypothesis with hypothesis testing at a .05 level of significance? Explain.

What is the value of the point estimate?

Answer 1

Answer:

Decision: Support the null hypothesis.

Sample mean: -12

Step-by-step explanation:

Hello!

When deciding with a Confidence interval you have to keep in mind that the following conditions are met:

• The hypothesis and the interval are made for the same parameter.
• The hypothesis should be two-tailed.
• The interval and the test have to have complementary confidence and signification levels. This means that if the interval is made with 1 - α= 0.95 the hypothesis test should be made with α= 0.05.

H₀: μ₁ - μ₂= 0

H₁: μ₁ - μ₂≠ 0

α: 0.05

If the interval contains the cero, it means that there is no difference between the means, so you support the null hypothesis.

If the interval doesn't contain the cero, there is a difference between the two means, so you reject the null hypothesis.

The intervals to estimate the population mean have the following structure:

Estimator ± Margin of error

This means that the sample mean (point estimate of the population mean) is in the middle of the calculated interval. To know it's the value you have to do a simple calculation:

sample mean: $\frac{Upper bound + Lower bound}{2}$

sample mean: $\frac{6 + (-30)}{2}$

sample mean: -12

I hope it helps!