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# GPCStatisticsChap 11

### Chaper 11 Statistics

What does it mean for a sampling method to be independent? What does it mean for a sampling method to be independent?
What does it mean for a sampling method to be dependent? A sampling method is dependent if the individuals selected for one sample are used to determine the individuals selected for the other sample. Dependent samples are often called matched-pairs samples.
Give an example of a dependent sampling method. A before-and-after study is a dependent sampling method. In this study, the same individual is studied before the treatment (such as a test review) and again after the treatment.
What is the first step when performing a hypothesis test or when finding a confidence interval for a dependent or matched-pair sample? Subtract each paired data values to form a list of differences. Then find the mean, d-bar, and the standard deviation, s-(sub d), of this list of differences.
What are the assumptions we will use when performing a hypothesis test or when finding a confidence interval on the difference of two means in a matched-pair sample? 1. The sample is obtained using a simple random sample. 2. The sample data are matched-pairs. 3. The differences are normally distributed with no outliers or the sample size, n, is large (n ≥ 30).
What is the null hypothesis when performing a hypothesis test for a matched-pair sample? H0: mean of the difference (mu-(sub d)) equales zero
What are the alternate hypotheses when performing a hypothesis test for a matched-pair sample? Two-Tailed: H1: mean of the difference is not zero ; Left-Tailed: H1: mean of the difference is less than zero; Right-Tailed: H1: mean of the difference is greater than zero.
How do you find the test statistic for a hypothesis test for a matched-pair sample? T0 = (mean of the sample differences) divided by ((standard deviation of the sample differences)/(square root of the sample size))
When you are sure that the differences are normally distributed with no outliers or the sample size, n, is large (n ≥ 30), how do you use a calculator to perform a hypothesis test for a matched-pair sample? Enter the data into two lists(or use STATS). Subtract the lists and store the result in a third list using the STO key. Then go to STAT over to TESTS and use #2 T-Test and the data from the third list of differences or statistics.
What are the decision criteria for the P-value method when performing a hypothesis test? If the P-value is < alpha, reject the null hypothesis. Otherwise do not reject the null hypothesis.
What is the lower bound for the confidence interval for a matched-pair study? (mean of the sample differences) – t-(sub alpha/2) X (standard deviation of the sample differences)/(square root of the sample size)
What is the upper bound for the confidence interval for a matched-pair study? Upper bound: (mean of the sample differences) + t-(sub alpha/2) X (standard deviation of the sample differences)/(square root of the sample size)
If zero is in the 90% confidence interval for the mean difference in a matched-pair study, is it possible that the means of the two variables are not equal? It is possible that the means from the two variables are not equal. You are only 90% confident that the differences of the means are even in the interval.
When you are sure that the differences are normally distributed with no outliers or the sample size, n, is large (n ≥ 30), how do you use a calculator to find the confidence interval for a dependent or matched pair study? Enter the data into two lists (or use STATS). Subtract the lists and store the result in a third list using the STO key. Then go to STAT over to TESTS and use #8 T-Interval and the data from the third list of differences.
To carry out our inference procedures on the difference of the two independent sample means, we will need to know the sampling distribution of the difference of the sample means. What is this? If the two populations are normally distributed or the two sample sizes are large (n1 ≥ 30 and n2 ≥ 30), then t =( (x1bar – x2bar) – (mu1 – mu2)) /SQUR(s1^2/n1 + s2^2/n2) approximately follows the Student's t-distribution.
What will we use for the degrees of freedom for the t-distribution for two independent samples? The smaller of n1 – 1 and n2 – 1 degrees of freedom. This is a conservative value. Calculators and computer programs use a different, less conservative value.
What assumptions do we make when performing inference tests (hypothesis tests or confidence intervals) on two independent samples? The samples are obtained using simple random sampling. The two samples are taken from two populations that are each normally distributed or the two sample sizes are large, (n1 ≥ 30 and n2 ≥ 30). The two population standard deviations are unknown.
What is the null hypothesis when performing a hypothesis test for independent samples? H0: mu1 = mu2
What are the alternate hypotheses when performing a hypothesis test for independent samples? Two-Tailed: H1: mu1 not equal to mu2 ; Left-Tailed: H1: mu1 < mu2; Right-Tailed: H1: mu1 > m2.
When you are sure that the assumptions are met, how do you use a calculator to perform a hypothesis test for independent samples? Enter the data into two lists (or use STATS option). Then go to STAT over to TESTS and use #4: 2 -SampT-Test. Choose NO for the Pooled option and use the names of the lists containing the data or the statistics.
When you are sure that the assumptions are met, how do you use a calculator to find a confidence interval for dependent samples? Enter the data into two lists (or use STATS). Then go to STAT over to TESTS and use #0 2-SampTInt. Choose NO for the Pooled option and use the names of the lists containing the data or the statistics.
What assumption are required for p̂1 - p̂2 to be normally distributed where p̂1 is the proprton from the first sample and p̂2 is the proportion from the second sample? The samples are independently found using simple random sampling, n1×p1×(1–p1) ≥ 10 and n2×p2×(1–p2) ≥ 10, and each sample is less than 5% of the population. Check that these assumptions are met before performing inference tests here.
What null hypothesis do we use when testing a hypothesis about the difference between two population proportions? H0: p1 = p2
What alternate hypotheses do we use when testing a hypothesis about the difference between two population proportions? Two tailed test H1: p1 ≠ p2; Left tailed test H1: p1 < p2; Right tailed test H1: p1 > p2.
Once the assumptions have been met, how can a calculator be used to perform a hypothesis test about the difference between two means? STAT to TESTS then #6 2-PropZTest and fill in the values and check that the P-value < alpha.
Once the assumptions have been met, how can a calculator be used to find a confidence interval for the difference between two means? STAT to TESTS then #B 2-PropZInt and fill in the values.
Created by: jessicacraig