Chapter 10 Flashcards
Null Hypothesis for Proportions
H0: p1−p2=0
Alternative Hypothesis for Proportions.
1) Ha: p1−p2<0 (or p1 < p2)
2) Ha: p1−p2>0 (or p1 > p2)
3) Ha: p1−p2≠0 (or p1 ≠ p2
Conditions for Proportion Test
a) Randomization.
b) sample size. There are at least 5 successes and failures in each group.
Test Statistic for Proportions
z- (p1)-p2)-/se
Standard Error for Comparing Two Population Proportions
Sqrt(p(1-p)(1/n1+1/n2))
Conclusions for Comparing Two Population Proportions
1) If P-value is less than a, reject H0. There is sufficient evidence, at a, that Ha is true
2) If the p-value is greater than a, fail to reject H naught. There is insufficient evidence, at a, that ha, is true.
What are the two tests for comparing two means?
1) Two sample t-test.
2) Paired t-test
Two-sample t-test
Used to test whether the average of two groups are the same for a quantitative variable.
Paired t-test
Used to investigate matched-pairs designs and is in fact a specialized version of a normal t-test
Null Hypothesis for Two Population Means
H0: μ1−μ2=0 (or μ1=μ2)
Alternative Hypothesis for Population Means
1) Ha: μ1−μ2<0 (or μ10 (orμ1>μ2)
3) Ha: μ1−μ2≠0 (or μ1≠μ2)
Conditions for Model (Means)
a) Randomization.
b) Sample size. Population distributions are nearly normal and n1 and n2 are greater than 30.
3) To use a two-sample test, the two groups we are comparing must be independent of each other.
Conclusion for Comparing Two Population Means
1) If P-value is less than alpha, reject H0. There is sufficient evidence, at alpha that Ha is true.
2) If P-value is greater than alpha, fail to reject h-naught. There is insufficient evidence, at alpha, that Ha is true.
Null Hypothesis for Paired t-test
H0: μd=0
Alternative Hypothesis for Paired t-test
1) Ha: μd<0
2) Ha: μd>0
3) Ha: μd≠0
Conditions for Paired t-test
a) Randomization
b) Sample size is nearly normal and n is greater than or equal to 30.
c) The two groups must be dependent on one another.
Test Statistic for Paired t-test
t = xd−0/ SE(xd)
Concussion for Paired t-tests
1) If P-value is less than alpha, reject null hypothesis. There is sufficient evidence at alpha that the alternative hypothesis is tur.
2) If the p-value is greater than alpha, fail to reject the null hypothesis. There is insufficient evidence at alpha that the alternative hypothesis is true.
Confidence Interval=
Point estimate plus or minus Critical Value * SE
What is the difference in calculating confidence intervals for comparing two groups?
Whereas we previously used ^por x as our point estimate for one-sample applications, our point estimates for these contexts will be ^p1−^p2 (for two-sample proportions), x1−x2 (for independent means), or xd (for paired applications.
Critical value is ___ for proportions or ____ for means
z, t
Matching confidence level to significance level α=
α=(100−c)100∨c=(1−α)∗100%
If the hypothesized value falls ____ the confidence interval, we would not reject the null hypothesis at the corresponding significance level.
Within
If the hypothesized value falls ____ the confidence interval, we would reject the null hypothesis at the significance level.
Outside.
