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Statistics Chapter 7
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Terms in this set (17)
Hypothesis Test
A process that uses sample statistics to test a claim about a value of a population parameter
Null Hypothesis
A statistical hypothesis that contains a statement of equality, such as less than or equal to, equal to, or greater than or equal to
Alternative Hypothesis
The complement of the null hypothesis. It is a statement that must be true if H0 is false and it contains a statement of strict inequality, such as less than, does not equal, or greater than
Writing the Hypothesis
To write the null and alternative hypotheses, translate the claim made about the population parameter from a verbal statement to a mathematical statement
Type I Error
Occurs if the null hypothesis is rejected when it is true
Type II Error
Occurs if the null hypothesis is not rejected when it is false
Level of Significance
In a hypothesis test, your maximum allowable probability of making a type 1 error. It is denoted by alpha. The probability of a type 2 error is denoted by beta. When you decrease alpha, you are more likely to be increasing beta.
Probability Value (P Value)
If the null hypothesis is true, a p value of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than one determined from the sample data
Decision Rule Based on P value
To use a p value to make a conclusion in a hypothesis test, compare the p value with alpha. #1 If p is less than or equal to alpha, then reject the null hypothesis. #2 If P > alpha, then fail to reject the null hypothesis
Finding the P value
After determining the hypothesis test's standardized test statistic and the test statistic's corresponding area, do one of the following to find the P value. #1 For a left-tailed test, P = area in left tail. #2 For a right-tailed test, P = area in right tail #3 For a two tailed test, P =2 (area in tail of test statistic)
Z Test for a Mean
A statistical test for the population mean. The z test can be used when the population is normal and sigma is known, or for any population when the sample size n is at least 30.
Test Statistic
The sample mean and the standardized test statistic is: ( x bar - meu) / (sigma / square root of n)
Rejection Region (Critical Region)
The range of values for which the null hypothesis is not probable. If a test statistic falls in this region, the null hypothesis is rejected.
Critical Value
Separates the rejection region from the non-rejection region
Finding Critical Values in a T-distribution
#1 Identify the level of significance (alpha). #2 Identify the degrees of freedom (n-1) #3 Find the critical value(s) using the table of values in the row with n-1 degrees of freedom.
If the hypothesis test is
a. left tailed, use the "One tail, alpha" column with a negative sign
b. right tailed, use the "One tail, alpha" column with a positive sign
c. two tailed, use the "two tails, alpha" column with a negative and a positive sign
T-test for a mean
The t-test for a mean is a statistical test for a population mean. The t-test can be used when the population is normal or nearly normal, sigma is unknown, and n < 30
Test statistic is x bar
Standardized Test Statistic is
T = (x bar - meu) / (s / square root of n)
Z Test for a Proportion
A statistical test for a population proportion p. The z-test can be used when a binomial distribution is given such that np is greater than or equal to 5 and nq is greater than or equal to 5.
Test Statistic is the sample proportion, p hat
Standardized Test Statistic is z = (p hat - meu sub p) / sigma sub p hat = (p hat - p) / square root of (pq / n)
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