Data analysis: Chapter 10: Two Sample Hypothesis Tests

The hypotheses for a right-tailed test for a mean difference ud look like:

H0: ud</ 0 vs. H1: ud> 0

When formulating a hypothesis test for comparing two variances, rather than calculating a difference, we calculate a ________.

ratio

When sample observations can be paired (or we have dependent samples) treating these as independent samples will _______.

reduce the power of the test

Test procedure for a two-sample test

state the hypothesis set up a decision rule insert the sample statistics make a decision

the t test statistic for a mean difference follows the ______ (use a letter) distribution with df = _____________ -1.

t; n

pooled variance

the common variance estimate from pooling the sample variances denoted as: s(2/p)

Does Jimmy's Market's average milk price difference from Jolene's Grocery's? The test statistic tcalc= -2.06. Find the p-value assuming variances are equal and given n1, and n2 are both 17.

.0476

Three questions to keep in mind when comparing two sample means

1. are the populations skewed? Are there outliers? 2. Are the sample sizes large (n >/ 30)? 3. Is the difference important as well as significant

One can approximate the t statistic using the z score if

1. the populations are not badly skewed 2. both sample sizes are 30 or more

The test statistic for testing equality of proportions ____

1. uses a pooled proportion to calculate the standard error 2. assumes when samples are large that p1-p2 is normally distributed 3. is a z-score

An accountant for a store is interested in comparing sales before and after an ad campaign. She expects an increase in sales after the campaign. The hypotheses would be _________.

H0: u1>/ 0; H1: did , 0 where d= says before - sales after

Two sample tests are used to compare sample results taken from two different ______.

populations

Two sample tests can be set up to compare old vs. _______, before vs. __________, or experimental vs. ________.

1. old vs. new 2. before vs. after 3. experimental vs. control

When choosing which test statistic to use for testing the difference of two means, which of the following are the three cases that one can choose?

1. population variances are unknown but assumed equal 2. population variances are unknown and not assumed equal 3. population variances are known

Order the steps in a two sample test

1. state the hypothesis 2. set up the decision rule 3. collect sample data and calculate a test statistic 4. make a conclusion

One can approximate the t statistic using the z score (and substituting s12 and s22 for the population variances) if ______

1. the populations are not badly skewed 2. both sample sizes are 30 or more

For a matched-pairs test for the difference in means, the Excel output allows us to use either the p-value approach or the _______.

critical value approach

If the same individuals are evaluated before and after a weight loss program, this is an examples of ______

a matched-pairs sample

For matched-pairs sampling, the parameter of interest is referred to as the mean ______.

difference

True or False: sample sizes must be equal when testing the difference between two means.

false

True or false: sample sizes must be equal when testing the difference between two means.

false

Select the method below which is NOT one fo the two types of matched-pairs samples.

independent samples from two populations

test statistic

the differenced between the sample statistic and the parameter divided by the standard error of the sample statistic. - the formula is determined by the sampling distribution of the sample statistic and whether or not we know the population variances.

When testing the difference between two means, the test statistic for cases 2 and 3 will be the same if the ________.

the same sizes are equal

When testing the difference between the two means, the test statistic for cases 2 and 3 will be the same if the _____.

the sample sizes are equal

True or False: Excel's paired t test provides the p-value for both a two-tailed and one-tailed test allowing the analyst to choose the appropriate value.

true

True or false: when testing the difference between two population means it is unlikely that one would know the value of the population variances.

true

When comparing two population proportions with the following sample results (p1=.24, p2=.28, n1=100, n2=200, and pc=.2667) the z test statistic would be _______. (round to two decimals.)

-.74

Which of the following describes a two sample test situation?

1. An agricultural study that compares the yield of two different crops 2. a marketing study that looks at purchasing patterns from two different demographic groups 3. an education study that looked at the change in freshman GPS's from one year to the next

In order to calculate the test statistic when the population variances are unknown and not assumed equal, the degrees of freedom can be calculated by:

1. using Welch's formula 2. df = min(n1-1, n2-1)

The hypotheses for a left-tailed test for a mean difference ud look like:

H0: ud >/ 0 vs. H1: ud< 0

The t test is considered _______ to mild violations of normality.

robust

Choose the correct statement about sample sizes when calculating a confidence interval for the difference in means

sample sizes do not need to be equal

If the population variances are unknown but assumed equal, the test is often called the _____ t test.

pooled

The hypotheses H0: u1-u2</ D0 & H1: u1-u2>D0 indicate a _____

right-tailed test

A specific type of dependent sampling when the sample observations are paired in some way is called _______

matched-pairs sampling

Does Jimmy's Market's average milk price differ from Jolene's Grocery's? The p-value = .0387 and alpha = .01

no, there is not significant evidence at a=.01 (p-value > .01) to conclude that there is a difference in average milk price

Hypothesis testing for comparing population means uses the difference (xbar1 - xbar2) where the samples are assumed to be taken from populations with a ______ distribution.

normal

two-sample tests

compare two sample estimates with each other, whereas one-sample tests compare a sample estimate with a non sample benchmark or target - especially useful because they possess a built in point of comparison

The parameter of interest for a matched-pairs sampling is _________

d=X1-X2

select the following menu choices for conducting a matched-pairs difference test with unknown variance:

data > data analysis > t-test: paired two samples for means > ok