Question

Imagine you're a researcher and you need to perform a two-sided test of an alternative hypothesis. You decide to conduct a significance test at the .05 level. The statistician in the next cubicle says you should use a 95% confidence interval for this hypothesis instead. Which of the following should you do?A. You should take the statistician's advice because a confidence interval is more accurate than a significance test.B. You should not take the statistician’s advice. Hypothesis testing relates to a single conclusion, while a confidence interval provides a range of plausible values for your population.C. You should take the statistician’s advice because a confidence interval takes longer than a significance test.D. You should not take the statistician’s advice. A one-sided significance test at the .05 level is equivalent to a 90% confidence interval.E. None of the above.

Answer 1

Answer:

B. You should not take the statistician’s advice. Hypothesis testing relates to a single conclusion, while a confidence interval provides a range of plausible values for your population.

Step-by-step explanation:

Hello!

A statistical hypothesis is an assertion or specification about the distribution of a random variable X, and, more specifically, about the parameters that characterize it. The objective of the hypothesis test is, therefore, to test the researcher's belief about the possible value of the parameter under study and obtain significant evidence to accept or reject it.

The objective of a Confidence interval is to estimate a possible range of values for the population parameter you are studying. If the confidence level is of 95%, this means that if you were to make 100 confidence intervals, you'd expect 95 of them to contain the true value of the parameter. But only with the confidence interval you cannot make any valid assertion about the parameter value.

In this case the study parameter is μ₁ - μ₂

The hypothesis is:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α 0.05

One of three valid methods to decide an hypothesis test is using a Confidence Interval. To do so the following conditions are to be met:

The hypothesis and CI should be made for the same population parameter.

The hypothesis should be two-tailed.

The signification level of the test "α" and confidence level of the interval "1 - α" have to be complementary.

For both is to be used the data from the same sample and same statistic.

If this conditions are met, the decision rule is:

If the value of the study parameter under the null hypothesis is included in the confidence interval, then you do not reject the null hypothesis.

If the value is not included in the interval, then you reject the null hypothesis.

To make a decision you need to do both, the interval and the two-tailed hypothesis.

I hope this helps!