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# Find critical value and test statistics for some t test questions

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1.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.

Right-tailed test, α = 0.1, n = 21
t0 = 2.528; t > 2.528
t0 = 1.323; t > 1.323
t0 = 1.325; t > 1.325
t0 = 1.325; t < 1.325

4.
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim μ > 33; α = 0.005. Sample statistics: = 34, s = 3, n = 25

t0 = -2.797, standardized test statistic ≈ -1.667, fail to reject H0; There is not sufficient evidence to support the claim
t0 = 2.797, standardized test statistic ≈ 1.667, reject H0; There is sufficient evidence to reject the claim
t0 = 2.797, standardized test statistic ≈ 1.667, fail to reject H0; There is not sufficient evidence to support the claim
5.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.
Left-tailed test, α = 0.1, n = 22
t0 = -2.518; t < -2.518
t0 = -1.321; t < -1.321
t0 = 1.323; t > 1.323
t0 = -1.323; t < -1.323

6.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.
Two-tailed test, α = 0.1, n = 23
t0 = -1.717, t0 = 1.717; t < -1.717, t > 1.717
t0 = -1.321, t0 = 1.321; t < -1.321, t > 1.321
t0 = -1.714, t0 = 1.714; t < -1.714, t > 1.714
t0 = 1.717; t > 1.717
7.
Find the standardized test statistic t for a sample with n = 10, = 16.5, s = 1.3, and if Round your answer to three decimal places.
-3.010
-2.189
-3.186
-2.617
8.
Find the standardized test statistic t for a sample with n = 12, = 21.7, s = 2.1, and if Round your answer to three decimal places.
-0.008
-0.825
-0.037
-0.381
9.
Find the standardized test statistic t for a sample with n = 12, = 31.2, s = 2.2, and α = 0.01 if Round your answer to three decimal places.
1.890
2.132
2.001
1.991

https://brainmass.com/statistics/type-i-and-type-ii-errors/critical-value-test-statistics-test-questions-613746

#### Solution Preview

1.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.

Right-tailed test, α = 0.1, n = 21
t0 = 2.528; t > 2.528
t0 = 1.323; t > 1.323
t0 = 1.325; t > 1.325
t0 = 1.325; t < 1.325
Just check t table, we find that to=1.325 and t>1.325 since right-tailed test.

4.
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim μ > 33; α = 0.005. Sample statistics: = 34, s = 3, n = 25

t0 = -2.797, standardized test statistic ≈ -1.667, fail to ...

#### Solution Summary

The solution gives detailed steps on find critical value and test statistics for some t test questions.

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