Chapter 10 - Two-Sample Tests

When comparing two populations with the following sample results the z test statistic would be _____. p1=.24 p2=.28 n1=100 n2=200 pc=.2667

-0.74

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?

-known variances -unknown variances assumed equal -unknown variances assumed unequal

Skipping a formal t test and simply using descriptive statistics can be a good choice if:

-the populations are heavily skewed -the sample sizes are small -there are extreme outliers

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

-the populations are not badly skewed -both sample sizes are 30 or more

The test statistic for testing equality of proportions:

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

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:

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

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

.0476

If no information is available about the population variances, one should choose Case _____ when testing the difference between means

3

T/F: Sample sizes must be equal when testing the difference between two means

False

Does Jimmy's Market's average milk price differ from Jolene's Grovery's? The p-value = 0.0387 and a = .01.

No, there is not significance 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 where the samples are assumed to be taken from populations with a ______ distribution

normal

In most cases, the hypothesized difference between two population means is ______.

null

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

sample sizes are equal

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 and not assumed equal, to calculate the test statistic we replace a2 and a2^2 with the ______ _______.

sample variances

Does Jimmy's Market charge less on average for milk than Jolene's Grocery?

sp2 = 0.0449, tcalc = -4.387

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

pooled

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

populations

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.

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

difference

The t test is considered ______ to mild violations of normaility

robust

T/F: Excel's paired t test provides for both a two-tailed and one-tailed test allowing the analyst to choose the appropriate value.

True

Examples of two-sample tests:

before vs after old vs new experimental vs control

Two-sample tests

compare two sample estimates with each other

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 population variances are unknown but assumed equal, the t test statistic uses a pooled _____ ______.

standard deviation

The test statistic for a mean difference follows the ___ distribution with df = ___ - 1.

t; n

Test procedure:

we state our hypotheses, set up a decision rule, insert the sample statistics, and make a decision