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54 Cards in this Set
- Front
- Back
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In statistics, a hypothesis is:
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a claim or statement about a property of a population.
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A hypothesis test or test of significance is:
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a procedure for testing a claim about a property of a population.
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What is the rare event rule for inferential statistics?
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If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
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The null hypothesis is denoted by:
The alternative hypothesis is denoted by: |
The null hypothesis is denoted by: H₀
The alternative hypothesis is denoted by: Hₐ or H₁ or H(subA) |
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The null hypothesis (H₀) is:
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a statement that the value of a population parameter (such as proportion, mean, or stdv) is EQUAL to some claimed value.
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The term null is used to indicate:
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no change or no effect or no difference
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The alternative hypothesis (Hₐ) is:
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the statement that the parameter has a value that somehow differs from the null hypothesis.
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The null hypothesis (H₀) always uses the these signs.
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equality signs: ≥, ≤, or =
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The alternative hypothesis (Hₐ) always uses these signs:
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> , < , or ≠
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If you are conducting a study and want to use a hypothesis test to support your claim, the claim must be worded so that:
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it becomes the alternative hypothesis Hₐ, and can be expressed using only the symbols: > , < , or ≠
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Can you ever support a claim that some parameter is equal to some specified value?
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No
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The alternative hypothesis (Hₐ) is sometimes referred to as the:
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research hypothesis
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What are the steps for identifying the null and alternative hypotheses?
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1) Express the original claim (OC) in symbolic form.
2) Express the counter claim (CC) symbolic form. 3) Label the two symbolic expressions as H₀ and Hₐ. |
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H₀ is the symbolic expression that contains:
Hₐ is the symbolic expression that does not contain: |
H₀ is the symbolic expression that contains: the equality
Hₐ is the symbolic expression that does not contain: equality. |
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H₀ is the symbolic expression that:
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the parameter equals the fixed value being considered.
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The test statistic is:
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a value used in making a decision about the null hypothesis.
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The test statistic is found by:
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converting the sample statistic (such as p̂, x̅, or s) to a score ( such as z, t, or χ²) with the assumption that the null hypothesis is true.
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The calculations required for a hypothesis test typically involve:
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converting a sample statistic to a test statistic.
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The rejection region or critical region is:
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the set of all values of the test statistics that cause us to reject the null hypothesis.
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The significance level is:
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the probability that the test statistic will fall in the rejection region when the null hypothesis is actually true.
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The significance level is denoted by:
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alpha (α)
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If the test statistic falls in the rejection region we:
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reject the null hypothesis.
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α is the probability of making the mistake of:
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rejecting the null hypothesis when it is true.
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A critical value is:
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any value that separates the rejection region (where we reject the null hypothesis) from the values of the test statistic that do not lead to rejection of the null hypothesis.
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To determine the type of test, we use the value of:
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Hₐ
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Describe the test for each one of the symbolic forms of the alternative hypothesis:
≠ < > |
≠ means a two-tailed test
< means a left-tail test > means a right-tail test |
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The P-value (P-v) is:
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the probability of getting a value of the test statistic that is AT LEAST AS EXTREME as the one representing the sample data, assuming the null hypothesis is true.
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Rejection region in the left tail: P-v =
Rejection region in the right tail: P-v = Rejection region in two tails: P-v = |
R.R. in the left tail: P-v = area to left of test statistic
R.R. in the right tail: P-v = area to right of test statistic R.R. in two tails: P-v = TWICE the area in the tail beyond the test statistic. |
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The null hypothesis is rejected if:
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the P-v is very small, such as 0.05 or less.
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If the P is low:
If the P is high: |
If the P is low, the null must go
If the P is high, the null will fly. |
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Describe each symbol:
≤ ≥ ≠ |
≤ means "no more than"
≥ means "no less than" ≠ means "different from" |
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Our initial conclusion of a hypothesis test is one of the following:
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1) Reject the null hypothesis
2) Fail to reject the null hypothesis |
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The decision to reject or fail to reject the null hypothesis usually made using either:
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the P-v method or the classical method
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Sometimes the decision to reject or fail to reject the null hypothesis is based on:
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confidence intervals
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Describe the P-v method for rejecting or failing to reject the null hypothesis:
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Using the significance level α:
If P-v ≤ α, reject H₀. If P-v > α, fail to reject H₀ |
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Describe the classical method for rejecting or failing to reject the null hypothesis:
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If the test statistic falls within the rejection region, reject H₀
If the test statistic doesn't fall within the rejection region, fail to reject H₀. |
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How are confidence intervals used to reject or fail to reject the null hypothesis?
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If a confidence interval does not include a claimed value of a population parameter, reject that claim.
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Can we ever "accept the null hypothesis?"
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No, we can only fail to reject the null hypothesis.
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can we ever prove a null hypothesis?
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No
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What is the statement to reject H₀ when the original claim contains an equality?
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"There is sufficient evidence to warrant rejection of the claim that... (state original claim).
This is the only case in which the original claim is rejected. |
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What is the statement to fail to reject H₀ when the original claim contains an equality?
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"There is not sufficient evidence to warrant rejection of the claim that...(state original claim).
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What is the statement to reject H₀ when the original claim does not contain an equality and becomes Hₐ?
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"The sample data support the claim that...(state original claim).
This is the only case in which the original claim is supported. |
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What is the statement to fail to reject H₀ when the original claim does not contain an equality and becomes Hₐ?
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"There is not sufficient sample evidence to support the claim that...(state original claim).
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What is a Type I error?
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Rejecting a True Null Hypothesis
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The probability of a Type I error is represented by the symbol:
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α
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What is a Type II error?
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Failing to Reject a False Null Hypothesis
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The probability of a Type II error is represented by the symbol:
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β
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α =
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The probability of a type I error
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β =
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The probability of a type II error
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What are the steps for the P-v method of hypothesis testing?
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1) Identify the (OC), (CC), H₀, and Hₐ.
2) Find the test statistic and P-v. 3) Draw graph and show test statistic and P-v. 4) Evaluate the P-v in regards to α. 5) Make statement |
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What are the steps for the classical method of hypothesis testing?
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1) Identify the (OC), (CC), H₀, and Hₐ.
2) Find the test statistic, critical values, and rejection region. 3) Draw graph and show test statistic, critical value, and rejection region. 4) Make statement |
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What are the steps for the C.I. method of hypothesis testing?
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1) For two-tailed test, construct a C.I. of 1 − α.
For one - tailed test, construct a C.I. of 1 − 2α. 2) Reject claim for a value of a population parameter that is not included in the C.I. limits. |
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The power of a hypothesis test is:
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the probability (1 − β) of rejecting a false null hypothesis.
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A power of at least ___ is a common requirement for determining that a hypothesis test is effective.
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0.80
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