Chapter 10

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

-0.74

Does Jimmy's Market's average milk price differ 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.

0.0476

For a left-tailed test for the following null hypothesis H0: π1 - π2 ≥ .20, the z test statistic = -.75. The p-value for this test is

0.2266

Which of the following describes a two sample test situation?

1. An education study that looked at the change in freshmen GPAs from one year to the next. 2. An agriculture study that compares the yield of two different crops. 3. A marketing study that looks at purchasing patterns from two different demographic groups.

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

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

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

To conduct an F test in Excel one can

1. choose the function =F.TEST(array1, array2) 2. Choose Data > Data Analysis > F-Test Two Sample Variances

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. df = min(n1 - 1, n2 -1) 2. using welches formula

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

1. population heavily skewed 2. outliers 3. sample sizes are small

Order the steps in a two sample test.

1. state the hypothesis 2. set up decision rule 3. calc sample statistic 4. make conclusion

The criteria for assuming normality of p1 - p2 is that both np and n(1-p) for each sample is greater than or equal to

10

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

3

When conducting a two-tailed F test for the comparison of means, given that n1 = 10, n2 = 8, and α = .05, FR = ________ and FL ___________

4.82, 0.24

To find the two-tailed p-value for an Fcritical < 1 one would use

=2*F.DIST(Fcritical, df1, df2, 1)

To calculate a right-tailed probability for a specific F value in Excel

=F.DIST.RT(Fcalc, df1, df2)

To find the lower critical value of the F statistic with alpha = .05, df1 = 12 and df2 = 7, use the Excel function

=F.INV(.025, 12,7)

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

Data > Data Analysis > t-test: Paired Two Sample for Means > OK

Inference regarding the ratio of sample variances uses the _______ distribution which is based on a family of distributions depending on the separate degrees of freedom.

F

For a left-tailed test for the following null hypothesis H0: π1 - π2 ≥ .20, the p-value = .2266. Given that α = .10, the correct conclusion would be

Fail to reject H0. There is not significant evidence to conclude the difference in proportions is less than .20.

The test statistic for the hypothesis test of the ratio of two population variances is

Fdf1,df2 = s12 s22

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

H0: μd ≤ 0 vs H1: μd > 0

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

H0: μd ≥ 0 vs H1: μd < 0

When testing if population proportions are different, the hypotheses are

H0: π1 - π2 = 0 vs H1: π1 - π2 ≠ 0

Choose the correct formulation for a right-tailed test for non-zero difference in proportions.

H0: π1 - π2 ≤ D0 vs H1: π1 - π2 > D0

If an analyst believes Fund 1 is riskier than Fund 2, the appropriate hypotheses she would use to verify this are

H0: σ12/σ22 ≤ 1; H1: σ12/σ22 > 1

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

Independent samples from two populations

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

robust

The F distribution assumes populations are

normal

The F statistic requires two degrees of freedom: df1 is the degrees of freedom for the _________ and df2 is the degrees of freedom for the _______

numerator, denominator

If the population variances are unknown and not assumed equal, to calculate the test statistic we replace σ12 and σ22 with the _______ ________

sample variances

A researcher finds that 15 out of 45 customers of store 1 feel they get good service where 20 out of 40 customers in store 2 feel they get good service. The sample proportions are

p1 = .33 for store 1 and p2 = .50 for store 2

Two sample tests are used to compare sample results taken from two populations with different _______ values

parameter

When comparing two population proportions with the following sample results (p1 = .24, p2 = .28, n1 = 100, n2 = 200) the pooled proportion would be

pc = 24+56 100+20024+56100+200 = .2667

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

pooled

The Fdf1,df2 distribution is

positively skewed.

When using a confidence interval to test for difference in means, using equal or balanced sample sizes will increase the _________ of the test.

power

`If we know that 90 out of100 customers in a grocery store chain prefer having their groceries bagged for them, we would express this parameter as a population

proportion

When comparing the percentage of satisfied customers between Dell and HP one would analyze the difference between population

proportions

To test the equality of variances the F statistic calculates the ______ of two sample variances.

ratio

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.

The hypotheses H0: μ1 - μ2 ≤ D0 & H1: μ1 - μ2 > D0 indicate a

right-tailed test

The formula for calculating the confidence interval for a mean difference is

d� ± tα/2sdn

Two sample hypothesis tests compare two sample estimates with

each other

When testing the difference in means, ______ sample sizes can offer some advantages

equal

For unknown variances and large samples, approximation of the t statistic using the z score decreases Type I risk.

false

True or false: A confidence interval can be used to conduct a right-tailed test provided the α values are the same.

false

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

false

True or false: The F test does not assume the populations being sampled have a normal distribution.

false

True or false: The steps in a two sample hypothesis test are twice the number of steps in a one sample hypothesis test.

false

True or false: When testing for a non-zero difference in proportions we would still calculate a pooled proportion.

false

A statistically significant result would be important if the mean difference is

large enough.

The folded F test requires that we put the _____ sample variance in the numerator of the test statistic.

larger

The hypotheses H0: μ1 - μ2 ≥ D0 & H1: μ1 - μ2 < D0 indicate a

left-tailed test.

Two sample tests can be set up to compare old vs __________ before vs _________ or experimental vs __________

new, after, control

Hypothesis testing for comparing population means uses the difference (x�1 - x�2) where the samples are assumed to be taken from populations with a ______ distribution

normal

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 same individuals are evaluated before and after a weight loss program, this is an example of

a matched-pairs sample.

When collecting sample proportion data a success is defined as

any event of interest

Treating paired data as independent samples ignores the variation ________ paired values.

between

If normality of p1 - p2 cannot be assumed then the test must be conducted using the

binomial distribution.

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.

The parameter of interest for a matched-pairs sampling is

d = X1 - X2

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

difference

Does Jimmy's Market charge less on average for milk than Jolene's Grocery? To answer this question the following hypotheses were tested: H0: μ1 - μ2 ≥ 0 vs. H1: μ1 - μ2 < 0 where Jimmy's Market is population 1. Assuming σ12 and σ22 are unknown but equal and given the following sample information (x�1 = $3.20, x�2 = $3.56, s1 = $0.25, s2 = $0.15, n1 = 15, and n2 = 12) choose the correct test statistic calculation.

sp2 = 0.0449, tcalc = -4.387

If the population variances are unknown but assumed equal, the t test statistic uses a pooled

standard deviation

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

t, n

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

the sample sizes are equal.

If the Excel output for a matched pairs right-tailed test shows the t stat = 3.4551 and the t critical value is shown as 1.721 at α = 0.05 then the decision would be

to reject the null hypothesis because 3.4551 > 1.721.

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: The formula for a confidence interval for the difference in population means when population variances are unknown but assumed equal, incorporates a pooled estimate of the common variance.

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 testing differences in population proportions, one can set up a left-tailed test, a right-tailed test, or a

two

The folded F test is used to conduct a ________ -tailed test, simplified with only __________ critical value for F, found using α/2.

two, one

The hypotheses H0: μ1 - μ2 = D0 & H1: μ1 - μ2 ≠ D0 indicate a

two-tailed test

A manufacturer may want to compare the reliability of two products by comparing the ________ of their product characteristics.

variances

Inference concerning the ratio of 2 population variances is used to determine relative variability or, in the context of finance,

volatility.

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

zero

We combine, or pool, the sample proportions into one "big" sample when testing for _______ difference between population proportions.

zero