Ch. 10

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

between

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

matched-pairs sampling.

Hypothesis testing for comparing population means uses the difference (x̄1 - x̄2) where the samples are assumed to be taken from populations with a _________ distribution

normal

The formula for calculating a pooled sample proportion is

pc= (x1+x2) / (n1+n2)

When testing the difference in two means, if the sample sizes are 60 and 80 and the sample variances are close in value, then one could approximate the ___________ score with the _________ score

t-score; normal score

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

the sample sizes are small, the populations are heavily skewed and there are extreme outliers.

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

two-tailed test.

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 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

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.

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 steps in a two sample hypothesis test are twice the number of steps in a one sample hypothesis test.

False

The hypotheses to determine whether the average AAA battery life for Brand A differs from Brand B are

H0: μ1-μ2=0 & H1: μ1-μ2≠0

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

Independent samples from two populations

A confidence interval estimate for the difference in customer satisfaction rates between May and June of last year is -.14 ± .03. Which statement below is most appropriate?

It appears that the customer satisfaction rate decreased from May to June.

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?

Population variances are known, population variances are unknown but assumed equal and population variances are unknown and not assumed equal.

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

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

-.74

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

.2266

The statistic (S12) / (S22) follows what distribution if independent samples are drawn from normal populations with equal variances?

Fdf1,df2 distribution

True or false: An F test for two samples can be found under Excel's Data Analysis Toolpak.

True

To conduct an F test in Excel one can

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

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

difference

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

equal

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

robust

The test statistic for testing non-zero difference in proportions would be

zcalc = (p1−p2−D0) / (p1(1−p1)/n1)+(p2(1−p2)/n2)

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

zero

Which is the correct formula for the margin of error for a confidence interval for the different between two proportions?

zα/2 sq[ (p1(1−p1)/n1) + (p2(1−p2)/n2) ]

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.

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

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

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

4.82; 0.24

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)

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

False

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

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 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

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.

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

variance

Which of the following describes a two sample test situation?

An agriculture study that compares the yield of two different crops, a marketing study that looks at purchasing patterns from two different demographic groups and an education study that looked at the change in freshmen GPAs from one year to the next.

When setting up a two-tailed hypothesis test for comparing two variances, the correct formulation is:

H0: (σ12/σ22) = 1 vs H1: (σ12/σ22) ≠ 1

If we would like to test whether or not two population proportions differ by at least .30, the null hypothesis will state:

H0: π1 - π2 ≥ .30 vs H1: π1 - π2 < .30

When collecting sample proportion data a success is defined as

any event of interest

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

binomial distribution.

The parameter of interest for a matched-pairs sampling is

d = X1 - X2

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

dbar ± tα/2[sd/sq(n)]

Samples might show statistically significant differences but a company's financial expert can tell you if the difference is

important

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

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 (15/45) for store 1 and p2 = .50 (20/40) for store 2

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+200) = .2667

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

proportions

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

ratio

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 and is a z score

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

volatility

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

populations

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

reduce the power of the test.

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.

In comparing two population proportions, our parameter of interest is

π1 - π2