Graphical Analysis In Exercises 9–12, state whether each stand...

Question

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.

a. t = -1.755

Graph of a t-distribution showing critical values at -1.725 and 1.725, with shaded areas indicating rejection regions.

Accepted Answer

Hello everyone. Let's take a look at this question together. In a statistical test, the calculated test statistic is T, which is equal to -1.621. Does this value indicate that you should reject the null hypothesis? And here we have a graph showing our statistical test, and we want to know, is it answer choice A, we fail to reject the null hypothesis, or answer choice B, we reject the null hypothesis. So, in order to solve this question, we have to recall what we have learned about statistical tests to determine based on our image that we are provided, and a calculated test statistic that is equal to -1.621, does this value indicate that we should reject The null hypothesis. And so the first step in solving this problem is analyzing the image that we are given, which based on the image, we know that the image shows a two-tailed hypothesis test with critical values at positive and negative 1.538. And we also know that the rejection regions are four values of the test statistic that are less than -1.538, or greater than 1.538, and are represented as the green shaded tails in the image. And lastly, the acceptance region where we fail to reject the null hypothesis lies between -1.538 and 1.538, which is the orange shaded central region in the image. And so from the provided information, we know we are given our T, which is equal to -1.621, which this value is less than -1.538, therefore, it falls in the rejection region. So in conclusion, given our test statistic and the image, we know that we reject the null hypothesis. As our test statistic of -1.621 is less than -1.538, so it falls in the rejection region, and we reject the null hypothesis. Therefore, answer choice B, reject the null hypothesis is the correct answer. And all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.

a. t = -1.755

Key Concepts

Null Hypothesis and Alternative Hypothesis

Critical Values and Rejection Regions

Standardized Test Statistic (t-value)

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