Rejection Region and Critical Values

What type of error is committed when a true hypothesis is rejected?

It is the number of possible combinations of decisions and truth values of null hypothesis when we perform hypothesis testing.

Which of the statement/s above illustrates a Type I error? I. A boy whose height is 5’2” insists that his height is just 5’6”. II. A police officer accepts unsolicited gifts even if it is wrong to do so. III. Danilo still insists on working illegally despite knowing its risks. IV. Julia says that her hair color is not black, instead tells that she has dark-skinned.

Which of the statement/s above illustrates a Type II error? I. A boy whose height is 5’2” insists that his height is just 5’6”. II. A police officer accepts unsolicited gifts even if it is wrong to do so. III. Danilo still insists on working illegally despite knowing its risks. IV. Julia says that her hair color is not black, instead tells that she has dark-skinned.

Population standard deviation is known, and the confidence level is 90% for a two-tailed test.

Population standard deviation is unknown, the confidence level is 95% for a two-tailed test and the sample size is 16.

Sample size is 150 but the population standard deviation is unknown, and the confidence level is 90% for a two-tailed test.

Population standard deviation is unknown, the confidence level is 90% for a two-tailed test and the sample size is 10.

A certain test statistic lies in the rejection region, which of the following must be true? A. The test statistic is equal to the critical value. B. The test statistic is less than the critical value. C. The test statistic is greater than the critical value. D. The critical value is greater than the test statistic.

A sample of 250 bulbs were taken to verify the claim of its manufacturer that the average lifespan of their bulbs is 2.5 years. Which distribution must be considered to identify the appropriate rejection region?

A sample of 250 bulbs were taken to verify the claim of its manufacturer that the average lifespan of their bulbs is 2.5 years. What must be the critical value if the claim will be tested using 99% level of confidence?

A sample of 250 bulbs were taken to verify the claim of its manufacturer that the average lifespan of their bulbs is 2.5 years. Assuming that a test statistic was determined to be 2.11. Does this value lie on the rejection region?

A random sample of Grade 11 students were selected from a population whose standard deviation is unknown. Which distribution must be considered to identify the appropriate rejection region?

Suppose that there were 25 students, what will be the critical value if α = 0.01?

Suppose that there were 25 students, what will be the critical value if α = 0.01 and the test statistic was computed as 2.93. Does this value lie on the rejection region?