Week 9 - Significance Tests: The Basics Tests About a Population Proportion

Question 1

Significance Test

Answer 1

A formal procedure for comparing observed data with a claim.

Question 2

Null Hypothesis (H0)

Answer 2

The claim tested by a statistics test; the null hypothesis is one we
are testing against. It is often a statement of “no difference” from the hypothesized value

Question 3

Alternative Hypothesis (Ha)

Answer 3

The claim about the population that we are trying to find evidence for.

Question 4

One-Sided

Answer 4

The alternative hypothesis is one-sided if we are testing that a parameter value is larger than or is smaller than (but in one direction only) than the null hypothesis
value.

Question 5

Two-sided

Answer 5

The alternative hypothesis is two-sided if we are testing that a parameter is different from the null hypothesis value.

Question 6

P-value

Answer 6

The probability, assuming H0 is true, that a statistic (such as p hat or x bar) would take a value as extreme or more extreme as the one actually observed. The smaller the Pvalue, the greater the evidence against H0.

Question 7

Statistically Significant

Answer 7

If the P-value is smaller than a pre-chosen value a, we say that the data is statistically significant at level a. In that case, we would reject H0 and
conclude that there is convincing evidence in favor of Ha.

Question 8

Type I Error

Answer 8

If we reject H0 when H0 is actually true.

Question 9

Type II Error

Answer 9

If we fail to reject H0 when H0 is actually false.

Question 10

Power

Answer 10

The power of a test against a specific alternative is the probability that the test will reject H0 at a chosen significance level a when the specified alternative value of of
the parameter is true.