Question

α is the probability of a Type I error, which occurs when we accept the alternative H1 when the null hypothesis Ho is true.

True False

A Type II error occurs when when a false null hypothesis is rejected.

True False

If a null hypothesis is rejected at the 5% significance level but not at the 1% significance level, then the p-value of the test is less than 1%.

True False

The power of a test is the probability of accepting a null hypothesis that is false.

True False

True or false. If the p-value is 4%, then we reject the null hypothesis and accept the alternative hypothesis at a significance level of 5% but not at a significance level of 10%.

True False

Answer 1

.Question: α is the probability of a Type I error, which occurs when we accept the alternative H1 when the null hypothesis Ho is true.

Ans. : TRUE.

EXPLANATION: When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. An α of 0.10 indicates that you are willing to accept a 10%chance that you are wrong when you reject the null hypothesis.

Question: A Type II error occurs when a false null hypothesis is rejected.

Answer: TRUE

EXPLANATION: A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. The rate of the type II error is denoted by the Greek letter β (beta) and related to the power of a test (which equals 1−β).

Question: If a null hypothesis is rejected at the 5% significance level but not at the 1% significance level, then the p-value of the test is less than 1%.

Answer: TRUE.

EXPLANATION:

The level of statistical significance is represented by p-value. Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p-value) of observing your sample results given that the null hypothesis is true.

Let, a p-value such as 0.05 (i.e., p = .05) i.e. that there is a 5% chance of finding a difference as large as the one in your study given that the null hypothesis is true. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .01, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.01 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to any trusted conclusion. Thus if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).

Question: The power of a test is the probability of accepting a null hypothesis that is false.

Answer: FALSE.

EXPLANATION: Power is the probability of rejecting the null hypothesis that is false. Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.

Question: True or false. If the p-value is 4%, then we reject the null hypothesis and accept the alternative hypothesis at a significance level of 5% but not at a significance level of 10%.

Answer : TRUE.

EXPLANATION :

The level of statistical significance is represented by p-value. Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p-value) of observing your sample results given that the null hypothesis is true.

When, a p-value is 0.04 (i.e., p = .04) i.e. that there is a 4% chance of finding a difference as large as the one in your study given that the null hypothesis is true. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. Where p = .04, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.04 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to any trusted conclusion.