hypothesis testing (2 sample)

• The two sample test is similar to the one sample test, except that we are now testing for differences between two populations rather than a sample and a population.
• There are three types of two sample tests: Hypothesis Testing with Sample Means (Large Samples), Hypothesis Testing with Sample Means (Small Samples), and Hypothesis Testing with Sample Proportions (Large Samples).
• The null hypothesis (H 0) is that the populations are the same.
• If the difference between the sample statistics is large enough, or, if a difference of this size is unlikely assuming that the H 0 is true, we will reject the H 0 and conclude there is a difference between the populations.
• The null hypothesis is a statement of “no difference”.
• The 0.05 level will continue to be our indicator of a significant difference.
• We change the sample statistics to a Z score, place the Z score on the sampling distribution and use Appendix A to determine the probability of getting a difference that large if the H 0 is true.
• The alternative hypothesis (Ha) in the 5-step method is P u1 < P u2.
• A 1-tailed test, with α =.05 and z= - 1.65, is used in the 5-step method.
• The question in the 5-step method asks "did the special program work?"
• The null hypothesis (Ho) in the 5-step method is Pu1 = Pu2.
• The z-distribution (z-test) is used in the 5-step method.
• The 5-step method includes steps 1-3: one random sample, the sample is large, and n1 + n2 ≥ 100, which is normal.
• If the difference in the 5-step method is significant and is not random chance, then the null hypothesis (Ho) is rejected.
• In the 5-step method, if z obtained < Z critical, then the null hypothesis (Ho) is rejected.
• The alternate hypothesis (H 1) is the research hypothesis.
• If the null hypothesis is rejected, then we will have found evidence to support the research hypothesis.
• As long as random samples are used, a test of significance must be conducted.
• The critical region is defined by the Z (critical) value of ±1.96.
• The middle class families seem to use email more but is the difference significant?
• Differences that are otherwise trivial or uninteresting may be significant.
• The use of one-vs. two-tailed tests results in a higher likelihood of rejecting the null hypothesis.
• The research hypothesis contradicts the null hypothesis and asserts there is a significant difference between the populations.
• The size of the sample (n) impacts the likelihood of rejecting the null hypothesis.
• Significance is not the same as importance.
• The sampling distribution is the Z distribution and the alpha (α) is 0.05.
• The difference between the email usage of middle class and working class families is significant (Z=19.74, α =.05).
• The cut-off between the middle section and +/- .025 is represented by a Z-value of +/- 1.96.
• When working with large samples, even small differences may be significant.
• The null hypothesis asserts there is no significant difference between the populations.
• The value of the test statistic is an inverse function of n.
• The test statistic (Z = 19.74) falls in the critical region so reject the null hypothesis.
• When α = .05, then .025 of the area is distributed on either side of the curve in area (C).
• To calculate P u (the pooled estimate the population proportion ( Pu ), the proportion of cases in the population that have the trait under consideration assuming the null hypothesis is true), the standard deviation of the sampling distribution is calculated as the difference between sample proportions divided by the square root of the number of samples minus one.
• The formula for proportions in hypothesis testing with sample proportions (large samples) is: P u = the pooled estimate of the population proportion ( Pu ), the proportion of cases in the population that have the trait under consideration assuming the null hypothesis is true, calculated as the difference between sample proportions divided by the standard deviation of the sampling distribution.
• Significance and importance are different things.
• In terms of efficiency ratings, as compiled by their superiors, how do the affirmative action employees rate? The ratings of random samples of both groups were collected, and the results are reported here (higher ratings indicate greater efficiency).
• Report t, df, and your α-level in your interpretation.
• The larger the n, the greater the value of the test statistic, the more likely it will fall in the critical region (region of rejection) and be declared significant.
• A number of years ago, the road and highway maintenance department of Sin City, Nevada, began recruiting minority group members through an affirmative action program.