What is the range of values of the test value that indicates that there is a significant difference?
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In our example concerning the mean grade point average, suppose we take a random sample of n = 15 students majoring in mathematics. Since n = 15, our test statistic t* has n - 1 = 14 degrees of freedom. Also, suppose we set our significance level α at 0.05, so that we have only a 5% chance of making a Type I error. Show
Right-TailedThe critical value for conducting the right-tailed test H0 : μ = 3 versus HA : μ > 3 is the t-value, denoted t\(\alpha\), n - 1, such that the probability to the right of it is \(\alpha\). It can be shown using either statistical software or a t-table that the critical value t 0.05,14 is 1.7613. That is, we would reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ > 3 if the test statistic t* is greater than 1.7613. Visually, the rejection region is shaded red in the graph.  Left-TailedThe critical value for conducting the left-tailed test H0 : μ = 3 versus HA : μ < 3 is the t-value, denoted -t(\(\alpha\), n - 1) , such that the probability to the left of it is \(\alpha\). It can be shown using either statistical software or a t-table that the critical value -t0.05,14 is -1.7613. That is, we would reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ < 3 if the test statistic t* is less than -1.7613. Visually, the rejection region is shaded red in the graph. Two-TailedThere are two critical values for the two-tailed test H0 : μ = 3 versus HA : μ ≠ 3 — one for the left-tail denoted -t(\(\alpha\)/2, n - 1)and one for the right-tail denoted t(\(\alpha\)/2, n - 1). The value -t(\(\alpha\)/2, n - 1) is the t-value such that the probability to the left of it is \(\alpha\)/2, and the value t(\(\alpha\)/2, n - 1) is the t-value such that the probability to the right of it is \(\alpha\)/2. It can be shown using either statistical software or a t-table that the critical value -t0.025,14 is -2.1448 and the critical value t0.025,14 is 2.1448. That is, we would reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ ≠ 3 if the test statistic t* is less than -2.1448 or greater than 2.1448. Visually, the rejection region is shaded red in the graph. 5. It is the range of the values of the test value which indicates that there is significant difference and that the null hypothesis H_0 should be rejected. a. Critical value b. Rejection region c. level of significance d. d. non-rejection or acceptance regionQuestion Gauthmathier7718Grade 11 · 2021-06-28 YES! We solved the question! Check the full answer on App Gauthmath 5. It is the range of the values of the test value which indicates that there is significant difference and that the null hypothesis
5. It is the range of the values of the test value - Gauthmath should be rejected. Gauthmathier4279Grade 11 · 2021-06-28 Answer Explanation Thanks (115) Does the answer help you? Rate for it! What the range of the values of the test value which indicates that there is significant difference and that the null hypothesis should be rejected *?A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.
Is the range of values of the test value that indicates?This is the range of values of the test value that indicates that there is a significance difference and that the null hypothesis should be rejected. It is denoted by H 1 H_1 H1 , is a statement that there is a difference between a parameter and a specific value, or that there is a difference between two parameters.
How do you know if at test is significant?If a p-value reported from a t test is less than 0.05, then that result is said to be statistically significant. If a p-value is greater than 0.05, then the result is insignificant.
Which test is used for testing the significance of mean difference?A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related.
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