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.
Right-Tailed
The 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-Tailed
The 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-Tailed
There 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 region
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Gauthmathier7718
Grade 11 · 2021-06-28
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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.
a. Critical value
b. Rejection region
c. level of significance
d. d. non-rejection or acceptance region
Gauthmathier4279
Grade 11 · 2021-06-28
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Explanation
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