Chap 10 Quiz

A p-value is a probability.

True The p-value of the probability of having a test statistic as extreme as, or more extreme than, the value observed, given that the null hypothesis is true.

The Greek letter used to represent the probability of a Type I error is alpha (α).

True Type I error is represented by the Greek letter alpha (α) and Type II error is designated by the Greek letter beta (β).

If the null hypothesis is µ ≥ 200, then a two-tail test is being conducted.

False A two-tailed test requires that the null hypothesis use the equal ( = ) sign. Rejection of the null can happen in either direction (i.e. a test statistic that is either too high, or too low). Anything other than equal (i.e. the null hypothesis is either, "greater than or equal to", or, "less than or equal to"), indicates a one-tailed test.

The researcher must decide on the level of significance after setting up the null hypothesis and alternate hypothesis, but before formulating a decision rule and collecting sample data.

True Selecting the level of significance is Step 2 in the hypothesis testing procedure, while formulating a decision rule is Step 4 and collecting sample data is Step 5. It is not ethical to collect data and then decide, after the fact, what the level of significance is in order to bias the decision in favor of your desired result.

An alternate hypothesis is a statement about a population parameter that is accepted if the sample data provide sufficient evidence that the null hypothesis is false and should be rejected.

True The alternate hypothesis describes what you will conclude if you reject the null hypothesis.

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

True The level of significance is the risk of making a Type I error (rejecting the null hypothesis when it is true) and, it is represented by the Greek letter alpha alpha (α).

If the null hypothesis is false and the researchers do not reject it, a Type I error has been made.

False A Type I error is rejecting the null hypothesis when it is true. A Type II error is not rejecting the null hypothesis when it is false.

An example of a NULL hypothesis is: A person is innocent until proven guilty.

True A hypothesis is a statement about a population parameter subject to verification.

A test statistic is a value, determined from sample information, used to decide whether to reject the null hypothesis.

True A test statistic is a value, determined from sample information, used to decide whether to reject the null hypothesis

A Type II error is the probability of rejecting the null hypothesis when it is actually true.

False A Type II error is not rejecting the null hypothesis when it is false. The probability of committing a Type II error is designated by the Greek letter beta (β). The probability of rejecting the null hypothesis when it is true is a Type I error and is represented by the Greek letter alpha alpha (α).

For a one-tailed test with a .05 level of significance, the critical z statistic is 1.645, while the critical t statistic is 1.96.

False It is impossible to know the t statistic without knowing the sample size from which to compute the degrees of freedom.

A p-value is the same as a stated significance level.

False The p-value is the probability of observing a sample value as extreme as, or more extreme than, the value observed from the sample taken, given that the null hypothesis is true. Whereas, the researcher sets the significance level prior to taking the sample. (Therefore, the likelihood that they would be the same is remote, at best.)

Hypothesis testing is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.

True The goal of hypothesis testing is to determine whether a statement about a population parameter is reasonable based on sample evidence and probability theory. If the statement is statistically determined to be not reasonable, we will reject this "Null Hypothesis". If the statement is not rejected, we are said to "fail to reject" the Null Hypothesis (BUT, that does not mean that the hypothesis is necessarily true, however.)

Assuming that the null hypothesis is true, a p-value is the probability of observing a sample value as extreme as, or more extreme than, the observed sample observation.

True The p-value is the probability of observing a sample value greater than or equal to (for the upper tail), or less than or equal to (for the lower tail) this value, assuming the null hypothesis is true.